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[Title]
202_Cs͑̕

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
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% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB


[Problem]
̖₢ɓB

[FontSize]
5
[Level1]
ꎟ͑i邩ߎZj
180~100~̂ɂ킹30CS2660~B
100~̂ɂ܂B

process
100~̂ɂ$x$ƂƁC80~̂ɂ$30-x$B\\
$80(30-x)+100x=2660$C$x=13$\\
iʁj̕\80~100~ɕς20~̍邩C\\
$260\div 20=13$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    100~ & 0 & $\cdots$ & $x$ \\ \hline
    80~ & 30 & $\cdots$ &  \\ \hline
    v & 2400~ &              &     \\ \hline
         & 260     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

13

l1l̓ꗿ900~Cw1l̓ꗿ500~̃X|[cZ^[ɁC
lƒw킹20lœꂵāC
12,800~xB
l̐l͉lB

process
l̐l$x$lƂƁC\\
$900x+500(20-x)=12800$\\
iʁj̕\500~900~ɕς400~̍邩C\\
$2800\div 400=7$l
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    900~ & 0l & $\cdots$ & $x$ \\ \hline
    500~ & 20l & $\cdots$ &  \\ \hline
    v & 10,000~ &              &     \\ \hline
         & 2,800     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

7l

80~؎100~؎킹18Ƃ̑́C
1600~łB80~؎͉̂B

process
80~؎$x$ƂƁC80~؎$(18-x)$B\\
$80x+100(18-x)=1600$\\
iʁj̕\80~100~ɕς20~̍邩C\\
$200\div 20=10$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    80~ & 0 & $\cdots$ & $x$ \\ \hline
    100~ & 18 & $\cdots$ &  \\ \hline
    v & 1800~ &              &     \\ \hline
         & 200     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

10

qǂŁClƎqǂ킹21le[}p[N֍sB
ꗿ͑l1200~Cqǂ800~ŁCS19,200~xB
̂ƂCqǂ͉lB

process
$800x+1200(21-x)=19200$\\
iʁj̕\1200~800~ɕς400~̍邩C\\
$6,000\div 400=15$l
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    800~ & 0l & $\cdots$ & $x$ \\ \hline
    1200~ & 21l & $\cdots$ &  \\ \hline
    v & 25,200~ &              &     \\ \hline
         & 6,000     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

15l

50~؎80~؎킹28Ƃ̑́C
1970~łB80~؎͉̂B

process
80~؎$x$ƂƁC80~؎$(28-x)$B\\
$80x+50(28-x)=1970$\\
iʁj̕\50~80~ɕς30~̍邩C\\
$570\div 30=19$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    80~ & 0 & $\cdots$ & $x$ \\ \hline
    50~ & 28 & $\cdots$ &  \\ \hline
    v & 1400~ &              &     \\ \hline
         & 570     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

19

P80~݂̂ƂP120~̃S܂B
݂ƃS킹16Az1,560~łB
S͉ŵł傤H

process
S$x$ƂƁC݂$(16-x)$B\\
$120x+80(16-x)=1560$\\
iʁj̕\80~120~ɕς40~̍邩C\\
$280\div 40=7$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    120~ & 0 & $\cdots$ & $x$ \\ \hline
    80~ & 16 & $\cdots$ &  \\ \hline
    v & 1280~ &              &     \\ \hline
         & 280     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

7

P50~݂̂ƂP80~̃S܂B
݂ƃS킹20Az1,240~łB
S͉ŵł傤H

process
S$x$ƂƁC݂$(20-x)$B\\
$80x+50(20-x)=1240$\\
iʁj̕\50~80~ɕς30~̍邩C\\
$240\div 30=8$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    80~ & 0 & $\cdots$ & $x$ \\ \hline
    50~ & 20 & $\cdots$ &  \\ \hline
    v & 1000~ &              &     \\ \hline
         & 240     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

8

50~؎80~؎킹17Ƃ̑́C
1180~łB80~؎͉̂B

process
80~؎$x$ƂƁC80~؎$(17-x)$B\\
$80x+50(17-x)=1180$\\
iʁj̕\50~80~ɕς30~̍邩C\\
$330\div 30=11$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    80~ & 0 & $\cdots$ & $x$ \\ \hline
    50~ & 17 & $\cdots$ &  \\ \hline
    v & 850~ &              &     \\ \hline
         & 330     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

11

̉ƂwZ܂ł1,320܂B܂12ŊwZɒȂ΂Ȃ܂B
͕190mC1170mi߂܂B
12ŊwZɒɂ͉ԑΗǂł傤H

process
̂$x$ƂƁC\\
$170x+90(12-x)=1320$\\
iʁj̕\Łuvuvɕς80m/̍邩C\\
$240\div 80=3$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    (170m/) & 0 & $\cdots$ & $x$ \\ \hline
    (90m/) & 12 & $\cdots$ &  \\ \hline
    v & 1,080m &              &     \\ \hline
         & 240m     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

3

PԂɓkł70mC
ł180m̑̐lC
Ƃ1850mꂽw܂ōŝ
17܂B
uv܂B

process
$x$ƂƁC\\
$180x+70(17-x)=1850$\\
iʁj̕\Łukvuvɕς110m/̍邩C\\
$660\div 110=6$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    (180m/) & 0 & $\cdots$ & $x$ \\ \hline
    k(70m/) & 17 & $\cdots$ &  \\ \hline
    v & 1,190m &              &     \\ \hline
         & 660m     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

6

1{200~̃W[X1{100~̃~lEH[^[v30{B
5000~xƂC肪800~łB~lEH[^[͉{B

process
~lEH[^$x${ƂƁCW[X$30-x${B\\
$100x+200(30-x)=4200$C$x=18$\\
iʁjv̒li4200~B̕\ŃW[X~lEH[^[ɕς100~̍邩C\\
$1800\div 100=18${
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    100~ & 0{ & $\cdots$ & $x$ \\ \hline
    200~ & 30{ & $\cdots$ &  \\ \hline
    v & 6000~ &              &     \\ \hline
         & 1800~     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

18{

Ƃ̑70mCƂ̑300m̐lC傤153350mꂽړIn܂ł߂ɂ́CԑȂ΂ȂȂB 

process
̂$x$ƂƁC\\
$300x+70(15-x)=3350$\\
iʁj̕\Łuvuvɕς230m/̍邩C\\
$2300\div 230=10$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    (300m/) & 0 & $\cdots$ & $x$ \\ \hline
    (70m/) & 15 & $\cdots$ &  \\ \hline
    v & 1,050m &              &     \\ \hline
         & 2,300m     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

10

T(4{)ƒ(2{)킹20CB̍v{64{̂ƂC߂͉H邩B

process
߂$x$HƂƁC\\
$2x+4(20-x)=64$\\
iʁj̕\ŋT߂ɕς2{̍邩C\\
$16\div 2=8$H
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    (2{) & 0H & $\cdots$ & $x$ \\ \hline
    T(4{) & 20C & $\cdots$ &  \\ \hline
    v & 80{ &              &     \\ \hline
         & 16{    &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

8H

߂ƋT킹32܂B
ꂼ̘̑a94ɂȂƂCT͉Cł傤H

process
T$x$CƂƁC\\
$4x+2(32-x)=94$\\
iʁj̕\ŋT߂ɕς2{̍邩C\\
$30\div 2=15$C
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    T(4{) & 0C & $\cdots$ & $x$ \\ \hline
    (2{) & 32H & $\cdots$ &  \\ \hline
    v & 64{ &              &     \\ \hline
         & 30{    &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

15C

50~؎80~؎킹18Ƃ̑́C
1230~łB80~؎͉̂B

process
80~؎$x$ƂƁC80~؎$(18-x)$B\\
$80x+50(18-x)=1230$\\
iʁj̕\50~80~ɕς30~̍邩C\\
$330\div 30=11$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    80~ & 0 & $\cdots$ & $x$ \\ \hline
    50~ & 18 & $\cdots$ &  \\ \hline
    v & 900~ &              &     \\ \hline
         & 330     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

11

100~؎50~؎킹40Ƃ̑́C
2750~łB100~؎͉̂B

process
100~؎$x$ƂƁC50~؎$(40-x)$B\\
$100x+50(40-x)=2750$\\
iʁj̕\50~100~ɕς50~̍邩C\\
$750\div 50=15$
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|c|c|c|c|c|} \hline
    100~ & 0 & $\cdots$ & $x$ \\ \hline
    50~ & 40 & $\cdots$ &  \\ \hline
    v & 2,000~ &              &     \\ \hline
         & 750     &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

15

߂ƋT킹22܂B
ꂼ̘̑a58ɂȂƂCT͉Cł傤H

process
T$x$CƂƁC\\
$4x+2(22-x)=58$\\
iʁj̕\ŋT߂ɕς2{̍邩C\\
$14\div 2=7$C
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    T(4{) & 0C & $\cdots$ & $x$ \\ \hline
    (2{) & 22H & $\cdots$ &  \\ \hline
    v & 44{ &              &     \\ \hline
         & 14{    &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

7C

߂ƋT킹13܂B
ꂼ̘̑a36ɂȂƂCT͉Cł傤H

process
T$x$CƂƁC\\
$4x+2(13-x)=36$\\
iʁj̕\ŋT߂ɕς2{̍邩C\\
$10\div 2=5$C
\begin{table}[!hbt]
  \begin{center}\begin{tabular}{|l|c|c|c|c|} \hline
    T(4{) & 0C & $\cdots$ & $x$ \\ \hline
    (2{) & 13H & $\cdots$ &  \\ \hline
    v & 26{ &              &     \\ \hline
         & 10{    &               &     \\ \hline
  \end{tabular}\end{center}
\end{table}

5C



















[Level2]
ꎟ͑ij
50~؎80~؎킹3480~wB
80~؎50~؎̖3{łB
w50~؎̖͉B

process
50~؎̖$x$ƂƁCӂ80~؎̖$3x$B
āC\\
$50x+80\times 3x=3480$\\
$5x+24x=348$B$x=12$\\

12

$25,000$~Z2lŕ̂ɁCZ͒̕̕2{$800$~ȂȂ悤ɂB
̂ƂCZ炤z͂炩B

process
̕$x$ƂƁC\\
$(2x-800)+x=25,000$\\
$x=8,600$BZ̕\\
$2 \times 8600-800=16,400$

16,400~

$92cm$̐jgāC̒c̒$4cm$`̂킭肽B
c̒ɂ΂悢B

process
c̒$x$ƂƁC̒$x+4$ƂȂB\\
$2 \{ x+(x+4) \}=92Bx=21$

$21cm$

l̎qǂɃNbL[𕪂̂ɁC$6$$40$]C$9$$2$ȂB
̂ƂCqǂ̐l͉lB

process
qǂ̐l$x$iljƂƁC\\
$6x+40=9x-2Bx=14$

14l

M̏N̏̊$7:3$łCMN$1,600$~n̂ŁC2l͓̏ɂȂB
M̂͂߂̏͂炩B

process
M̏$7x$CN̏$3x$ƂƁC\\
$7x-1600=3x+1600$\\
$x=800$B
M̂͂߂̏́C\\
$7 \times 800=5,600$~

5,600~

w̓wɂāCi҂͎󌱐$1/6$12lȂCsi҂͎󌱐85\%4lB
̂ƂCi҂͉lB

process
󌱎Ґ$x$lƂƁC\\
$\left( \displaystyle \frac{x}{6}-12 \right)+\left( \displaystyle \frac{85}{100} x+4 \right)=x$\\
$x=480$Bi҂$\displaystyle \frac{480}{6}-12=68$l

68l

bCC3lŎƂ$850$~̗v𓾂B
̗v𕪂̂ɁCozɉāCb͉2{C͕$80\%$ƂB
b󂯎z͂炩B

process
󂯎z$x$~ƂƁC\\
$1.6x+0.8x+x=850Bx=250$\\
b󂯎z\\
$1.6 \times 250=400$~

400~

Z̏ƒ̏̊$7:3$łCZ2,000~nƂC
2l͓̏ɂȂBẐ͂߂̏͂炩B

process
Ẑ͂߂̏$7x$Ĉ͂߂̏$3x$ƂƁCӂC\\
$7x-2000=3x+2000$\\
$x=1000$C$7x=7000$

7,000~

An_Bn_֍ŝɁC20km̎]ԂōsƁC4km̑ŕčs3Ԃ͂₭B
̂ƂCAn_Bn_܂ł̋߂B

process
An_Bn_܂ł̋$x$kmƂB\\
$\displaystyle \frac{x}{20}=\displaystyle \frac{x}{4}-3$C
$x=5x-60$C$x=\displaystyle \frac{60}{4}=15$km

$15$km

錎̃J_[̐j4񂠂Cׂ̐ĉ62ɂȂB
̌̍ŏ̐j͉B
iqgFŏ̐j$x$Ɛݒ肵Ȃj

process
$x+(x+7)+(x+14)+(x+21)=62$\\
$4x+42=62$

$5$

Ml̎qǂɕ̂ɁC1l7{3{ȂB
܂C1l6{1{]B
qǂ̐l߂B

process
$7x-3=6x+1$

4l

kɋʂẑɁC1l4
z18]C5z10ȂB
k߂B

process
k$x$ƂƁC\\
$4x+18=5x-10$

28l

NXŃyzƂC1l3{z60{]C
1l5{z10{sB
̃NX̐k̐l߂ȂB

process
k̐l$x$ƂƁC\\
$3x+60=5x-10$

35l

Ƃ1200mꂽw֌B
͂߂͖80m̑ŕĂCxȂ̂œr
110m̑őƂC12ɉwɒB
Ԃ߂B

process
߂鎞Ԃ$t$ƂƁC\\
$80t+110(12-t)=1200$

4

{[Ƃ锠pӂĂB
190{[ĂƁC17̃{[炸
cB
܂C100{[ĂƁC
Ō̔ɂ7ȂB
{[͑Sŉ邩B

process
̐$x$ƂƁC
$90x+17=100(x-1)+7$\\
$\therefore x=11$\\
{[̐
$90\times 11+17=1007$

1007

1{$x$~̉M12{C1000~oƂ̂肪280~łB
M1{̑߂ȂB

process
$12x+280=1000$~~~$x=\displaystyle\frac{720}{12}=60$

$60$~

鐔$x$$8${$7$ƁC$x$$4$3{ɓȂ܂B
鐔$x$߂ȂB

process
$8x+7=3(x+4)$

$1$









[Level3]
Ps͑̕
1150~̃S160~̃~J킹16C̑2,000~ȉɂB
Sł邾ꍇCS𔃂͂ɂȂ邩B

process
S𔃂$x$ƂƁCӂ\\
$150x+60(16-x) \leqq 2000$\\
$150x+960-60x \leqq 2000$\\
$90x \leqq 1040$\\
$x \leqq \displaystyle \frac{104}{9}=11.5c$B
$x=11$ 

11

1{120~̊ʃR[q[1{300~̉h{hN킹20{C
ʃR[q[͂ł邾ȂC4,000~ȉɂB
ʃR[q[{΂悢B

process
ʃR[q[$x${ƂƁC\\
$120x+300(20-x) \leqq 4000$\\
$x \geqq \displaystyle \frac{100}{9}=11.1c$

12{

1{100~̃{[y130~̏S킹30đ2,000~ȉɂB
{[y͍ő剽{邩B

process
{[y̐$x$ƂƁC\\
$100x+30(30-x) \leqq 2,000$\\
$x \leqq \displaystyle \frac{1100}{70}=15.c$

15{

݁CA4,500~CB2,800~̒B
ꂩ疈CA60~CB130~BB̒zCA̒zƓzȏɂȂ͉̂ォB

process
$x$ƂƁC\\
$4,500+60x \leqq 2,800+130x$\\
$x \geqq \displaystyle \frac{1700}{70}=24.c$

25

1{150~̃{[y1{60~̉M킹12{C1,500~ȉɂB
{[ył邾񔃂ɂ́C{[y{΂悢B

process
{[y$x${ƂƁC\\
$150x+60(12-x) \leqq 1,500$\\
$x \leqq \displaystyle \frac{780}{90}=8.66c$Bă{[y8{

8{

1{50~̉M180~̏S킹15C1,000~ȉɗ}B
S͍őŉ邩B

process
Š$x$ƂƁC\\
$50(15-x)+80x \leqq 1,000$\\
$x \leqq \displaystyle \frac{25}{3}=8.3c$B$x=8$

8

݁CZ7,000~C5,000~̒ĂB
NCZ1,200~C1,500~ĂƂC̒Z̒ƓzȏɂȂ͉̂NォB

process
$7000+1200x \leqq 5000+1500x$\\
$x \geqq \displaystyle \frac{20}{3}=6.c$B$x=7$

7N

P60~̃SƂP40~̃~J킹25Cv̑1250~ȓɂB̂ƂCS͍ő剽܂ŔƂł邩B

process
S̐$x$ƂB\\
$60x+40(25-x) \leqq 1250$\\
$x \leqq 12.5$

12

1{90~̉M{ƁC1150~̏S2Cv̑1000~ȓɂB̂ƂCM͍ő剽{܂ŔƂł邩H

process
M$x${ƂB\\
$90x+150 \times 2 \leqq 1000$\\
$x \leqq 7.77c$

7{

{[1Ii܂ƁjɂĂQ[B
{[IɓƂ̓_5_ŁC͂ꂽƂ̓_1_łB
̃Q[20sƂCv_70_ȏɂɂ́CŒች񓖂ĂȂ΂ȂȂB

process
$x$ƂB\\
$5x+1 \times (20-x) \geqq 70$\\
$x \geqq 12.5$

13

LfB[63Bqǂ1l3zƗ]肪10ȏɂȂB
̂ƂCqǂ̐l͍ő剽lƍl邩H

process
qǂ̐l$x$lƂB\\
$63-3x \geqq 10$\\
$x \leqq 17.66c$

17l

݁CA ̒ɂ1000~CB ̒ɂ300~ĂB
A ͖20~CB ͖50~ɒĂB
̂ƂCB ̒zA ̒z߂Ē͉̂ڂH

process
$x$ڂƂB\\
$1000+20x < 300+50x$\\
$x > 23.3c$

24

1200~̃P[L1100~̃v킹15C100~̔ɓB
̍v̑2000~ȓɂƂCP[L͍ő剽܂ŔƂł邩B

process
P[Ľ$x$ƂB\\
$100+200x+100(15-x) \leqq 2000$\\
$x \leqq 4.9$

4

鐔$x$3́C$x$23{菬B
𖞂$x$̒ŁCŏ̐߂B

process
$(x+3)<3(x-2)$ \\
$x > 4.5$

5

1̂𓊂āC1̖ڂoƂ̓_10_CȊO̖ڂoƂ̓_1_ƂB
̂30񓊂ƂCv_100_ȏɂɂ́C
1̖ڂ͍ŒችoȂ΂ȂȂH

process
1̖ڂ$x$Ƃ \\
$10x+1 \times (30-x) \geqq 100$\\
$x \geqq 7.77c$

8

1160~̃no[K[1100~̃h[ic킹20C
̍v2500~ȓɂB
̂ƂCno[K[͍ő剽܂ŔƂł邩H

process
no[K[̌$x$ƂB\\
$160x+100(20-x) \leqq 2500$\\
$x \leqq 8.33c$

8

o̓r[ʂ35C̓r[ʂ8ĂBoɃr[ʂĂC
õr[ʂ̌̃r[ʂ̌2{葽Ȃ悤ɂB
̂ƂCo͒Ƀr[ʂő剽܂ł邱Ƃł邩H

process
oɂ$x$ƂB\\
$35-x>2(8+x) $\\
$x<6.33c$

6

5炠鐔$x$2{́C$x$4傫B
̂悤$x$̂Ȃōő̐߂B

process
$2(5-x)>x-4$ \\
$x<4.66c$

4

1$600kg$̏d܂ŉ^ԂƂłGx[^ɁC̏d$80kg$̐lāC
1$30kg$̉ו^ԁB̂ƂCו1ɍő剽܂ŉ^ԂƂł邩H

process
$x$ƂƁC\\
$80+30x \leqq 600$\\
$x \leqq 17.33c$

17

P120~̃P[LāC100~̔ɂ߂ĂB
̍v1000~ȉɂBP[L͉܂Ŕ܂B

process
$120x+100 \leqq 1000$\\
$x \leqq \displaystyle \frac{900}{120}=\displaystyle \frac{15}{2}=7.5$

7

P180~̃P[LāC150~̔ɂ߂ĂB
̍v2,000~ȉɂBP[L͉܂Ŕ܂B

process
$180x+150 \leqq 2,000$\\
$x \leqq \displaystyle \frac{1,850}{180}=10.2c$

10

$4000$~̂ÂāCVnŗVԁBꗿ$600$~ŁC
蕨ACB2ނCA1350~CB1200~łB
ACB킹12ƂC蕨A͍ő剽܂ŔƂł邩B

process
A$x$ƂC\\
$600+350x+200(12-x) \leqq 4000$\\
$60+35x+20(12-x) \leqq 400$\\
$300+15x \leqq 400$C\\
$x \leqq \displaystyle \frac{100}{15}=6.c$

$6$

1$600kg$̏d܂ŉ^ԂƂłGx[^[ɁC̏d$80kg$̐lāC
1$30kg$̉ו^ԁB̂ƂCו1ɍő剽܂ŉ^ԂƂł邩B

process
ו̌$x$ƂƁC\\
$80+30x \leqq 600$\\
$x \leqq \displaystyle \frac{520}{30}=17.c$

$17$

o̓r[ʂ35C̓r[ʂ8ĂB
oɃr[ʂĂCõr[ʂ̌̃r[ʂ̌2{葽Ȃ悤ɂB
̂ƂCo͒Ƀr[ʂő剽܂ł邱Ƃł邩B

process
$x$C\\
ǒ$35-x$Č$8+x$B\\
$35-x > 2(8+x)$, \, $35-x> 16+2x$\\
$19>3x$, \, $x<\displaystyle \frac{19}{3}=6.c$

$6$

1160~̃no[K[1100~̃h[ic킹20C
̍v2500~ȓɂB
̂ƂCno[K[͍ő剽܂ŔƂł邩B

process
$160x+100(20-x)\leqq 2500$,\\
$160x+2000-100x \leqq 2500$\\
$60x \leqq 500$, \ $x\leqq \displaystyle \frac{500}{60}
=\displaystyle \frac{50}{6}=\displaystyle \frac{25}{3}=8.c$

$8$

|X^[J[Ɣ2ނňB
́CJ[140~C115~łB
J[Ɣ2ނ킹500C̍v15000~ȓɂB
̂ƂCJ[͍ő剽܂ň邱Ƃł邩B

process
$40x+15(500-x) \leqq 15000$\\
$40x+7500-15x \leqq 15000$\\
$25x \leqq 7500$\\
$x \leqq \displaystyle \frac{7500}{25}=300$

300

1̂𓊂āC1̖ڂoƂ̓_10_C
ȊO̖ڂoƂ̓_1_ƂB
̂30񓊂ƂCv_100_ȏɂɂ́C
1̖ڂ͍ŒችoȂ΂ȂȂB

process
1̖ڂ$x$oƂƁC\\
$10x+1 \times (30-x) \geqq 100$\\
$x \geqq \displaystyle \frac{70}{9}=7.c$\\

8

1200~̓1150~̗킹15C120~̔ɋl߂B
̑̍v3000~ȓɂƂC͍ő剽܂ŔƂł邩B

process
̌$x$ƂƁC\\
$200x+150(15-x) +120 \leqq 3000$\\
$x \leqq \displaystyle{63}{5}=12.6 \cdots$

12

100m1{̂ЂC5m3m2ނ̂Ђ킹25{؂蕪ƂC
5m̂Ђ͍ő剽{܂Ő؂蕪邱Ƃł邩B
CЂ͗]Ă悢̂ƂB

process
5m̂Ђ̖{$x${ƂƁC\\
$3(25-x)+5x \leqq 100$C
$x \leqq \displaystyle\frac{25}{2}=12.5$

12{

1000~̉Ԃт11{150~̉Ԃ{āC̍v3000~ȉɂB
̂ƂCԂ͍ő剽{܂ŔƂł邩B

process
Ԃ̖{$x${ƂƁC\\
$1000+150x \leqq 3000$C
$x \leqq \displaystyle\frac{40}{3}=13.\cdots$

13{

P_[X̃{[y𔃂߂1200~ēXɗƂC130~̃{[y80~̃{[yB
130~̃{[ył邾ƁC130~̃{[y12{\fbox{@@}{ɂȂB

process
130~̃{[y$x${ƂƁC\\
$130x+80\left( 12-x \right) \leqq 1200$\\
$x\leqq \displaystyle\frac{24}{5}=4.8$

S{

1200~̓1150~̗킹15A120~̔ɋl߂B
̑̍v3000~ȓɂƂA͍ő剽܂ŔƂł邩B

process
̌$x$ƂƁǍ$15-x$ƂȂB\\
$200x+150 (15-x) +120 \leqq 3000$\\
$20x+15(15-x)+12 \leqq 300$\\
$5x+237 \leqq 300$\,
$\therefore x \leqq \displaystyle\frac{63}{5}$

12

100m1{̂ЂA5m3m2ނ̂Ђ킹
25{؂蕪ƂA5m̂Ђ͍ő剽{܂Ő؂蕪邱Ƃł
邩BAЂ͗]Ă悢̂ƂB

process
5m̂Ђ̐$x${ƂƁA3m̂Ђ̐$25-x${ƂȂB\\
$5x+3\left(25-x \right) \leqq 100$\\
$\therefore x\leqq \displaystyle\frac{25}{2}=12.5$

12{

ÁA1̊{gp2000~ŁA1Ƃ̒ʘb25~gѓdbgĂB
1̊{gpƒʘb̍v5000~ȉɂB
̂ƂAA͍ő剽ʘb邱Ƃł邩B

process
ʘbԂ$x$ƂƁA\\
$25x+2000 \leqq 5000$\\
$\therefore x \leqq \displaystyle\frac{3000}{25}=120$

120

1{130~̃~NeB[1{100~̊ʃR[q[킹18{A
̑̍v2000~ȓɂƂA
~NeB[͍ő剽{܂ŔƂł邩B

process
~NeB̖{$x${ƂƁAʃR[q[̖{$18-x${ƂȂB\\
$130x +100 \left(18-x \right) \leqq 2000$\\
$\therefore x\leqq \displaystyle\frac{200}{30}=6. \cdot  \cdot \cdot$

6{

\hspace{8pt} 鐮$x$35{̂́A$x$7傫B
𖞂ŏ̐߂B

process
$5\left( x-3 \right)>x+7$\\
$x>\displaystyle\frac{22}{4}=\displaystyle\frac{11}{2}=5.5$

6

݂₰ŁA1280~َ̂qƁA1200~̃L[z_[킹15Ȃ̍v4000~ȓɂB
َq͍ő剽܂ŔƂł邩B

process
َq̌$x$ƂƁAL[z_[̌$15-x$ƂȂB\\
$280x+200\left( 15-x \right) \leqq 4000$\\
$x \leqq \displaystyle\frac{1000}{80}=12.5$

12

oXЂ̈Ԍ1600~łB
܂AoX̏ԂP񂲂Ƃɗxꍇ͋ψ260~łB
ɉ񂩃oXɏԂƂAԌ𔃂قA
oXxȂŏ̏ԉ񐔂͉񂩁B

process
ԉ񐔂$x$ƂƁA\\
$1600 < 260x$\\
$\therefore x> \displaystyle\frac{80}{13}=6.1\cdot \cdot \cdot$

7

Vn15000~̃t[pX𔃂@ƁAꗿ1000~𕥂A
1񂲂Ƃɏ蕨350~𔃂@B
t[pX̕ɂȂ̂́AŒችȏƂB
At[pXɂ͓ꗿ܂܂̂ƂB

process
߂񐔂$x$ƂƁA\\
$5000 < 1000+350x$\\
$\therefore x> \displaystyle\frac{80}{7}=11. \cdot \cdot \cdot$

12

oXЂ̈Ԍ1600~łB
܂CoX̏ԂP񂲂Ƃɗxꍇ͋ψ260~łB
ɉ񂩃oXɏԂƂCԌ𔃂قC
oXxȂŏ̏ԉ񐔂\fbox{\,C\,}łB

process
$1600 < 260x$\\
$x> 6.\cdots$

7

VnłP5000~̃t[pX𔃂@ƁCꗿ
1000~𕥂CP񂲂Ƃɏ蕨350~𔃂@B
t[pX̕ɂȂ̂́CŒ\fbox{\,CE\,}ȏƂłB
Ct[pXɂ͓ꗿ܂܂̂ƂB

process
$5000 \leqq 1000+350x$\\
$4000 \leqq 350x$~~~
$x \geqq \displaystyle\frac{80}{7}=11.\cdots$

12

݂₰ŁCP280~َ̂qƁCP200~̃L[z_[킹15C
̑̍v4000~ȓɂB
َq͍ő\fbox{\,CE\,}ƂłB

process
$280x+200(15-x) \leqq 4000$\\
$280x+3000-200x \leqq 4000$\\
$x \leqq \displaystyle\frac{1000}{80}=12.5$

12

d݂𓊂ĕ\oKi4îڂCo1îڂQ[B
d݂10񓊂ĊKi30iȏ̂ڂ邽߂ɂ́C\͏ȂƂ\fbox{\,C\,}ȏoȂ΂ȂȂB

process
\̉񐔂$x$ƂƁC\\
$4x+1\times(10-x) \geqq 30$\\
$3x \geqq 20$~~~
$x \geqq \displaystyle\frac{20}{3}=6.\cdots$

7

Xł͓700~𕥂ĉɂȂƁC
1500~̏i40~ŔƂłB
̏i𔃂ƂCȂƂ\fbox{\bf\,CE\,}ȏ㔃ƁC
ĔCȂŔȂB

process
$x$ƂĎxzׂB\\
$500x>460x+700$\\
$x>\displaystyle\frac{70}{4}=17.\cdots$

18

鐅ق̈ʂ̓ꗿ1l600~łB
C25lȏ̒ĉ1l500~œłB
25lɖȂĉłC25l̒c̗p̓ꌔw邱Ƃ
łꍇCȂƂ\fbox{\bf\,CE\,}lȏ̂Ƃ́C
c̗p̓ꌔwꌔ̑zȂB

process
$600x>500\times 25$\\
$x>20.8$

21l

1700~̖̓ٓ1500~̃no[Oٓ킹12āC
̍v7500~ȉɂB̂ƂC̓ٓő\fbox{\bf\, C \,}
ƂłB

process
$700x+500(12-x)\leqq 7500$\\
$x\leqq 7.5$

$7$

13炠鐔$x$́C$x$3{傫B
̂悤Ȑ̂Cő̐\fbox{\,\bf C\,}łB

process
$13-x>3x$C$x<\displaystyle\frac{13}{4}=3.\cdots$

$3$

1120~̃P[L190~̃ACX킹50ƂɂB
̍v5000~ȉɂƂCP[L͍ő剽Ƃł邩B

process
$120x+90(50-x) \leqq 5000$\\
$x \leqq \displaystyle\frac{500}{30}=16.\cdots$

16

Rԕ̂ƒł́C~Gi11$\sim$3jɒg[Ƌ̂
wĂB
11ɂāCwg[pƂ18LgpC
c̓̔pɎgpB
p̓30LȏɂƂC
w铔͍Œ\fbox{\bf\, CE \,}LłB

process
w铔$x$LƂƁC\\
$\displaystyle\frac{x-18}{2}\geqq 30$C
$\therefore x\geqq 78$

$78$






[Level4]
Q͑̕
ς72łCA2̐߂B

process
A2C$x$C$x+1$ƂƁC\\
$x(x+1)=72$B$x^2+x-72=0$B$(x+9)(x-8)=0$B$x=-9,8$\\
$(x,x+1)=(-9,-8),(8,9)$

$(-9,-8),(8,9)$

ς56łCA2̐߂B

process
A2C$x$C$x+1$ƂƁC\\
$x(x+1)=56$B$x^2+x-56=0$B$(x+8)(x-7)=0$B$x=-8,7$\\
$(x,x+1)=(-8,-7),(7,8)$

$(-8,-7),(7,8)$

a15ŁCς54ł2̐߂B

process
߂鐮$x$C$y$ƂƁC\\
$x+y=15$c\textcircled{\small 1}\\
$xy=54$c\textcircled{\small 2}\\
\textcircled{\small 1}$y=15-x$c\textcircled{\small 1}'\\
\textcircled{\small 1}'C\textcircled{\small 2}$x(15-x)=54$B$x^2-15x+54=0$\\
$(x-6)(x-9)=0$B$x=6,9$

$6,9$

̐̐B̓̐̍2łCꂼ2悵̘a130łB
̂ƂC傫̐߂B

process
傫$x$C$y$Ƃ\\
$x-y=2$@c\textcircled{\small 1}\\
$x^{2}+y^{2}=130$@c\textcircled{\small 2}\\
\textcircled{\small 1}C $y=x-2$ \textcircled{\small 2}ɑāC\\
$x^{2}+(x-2)^{2}=130$\\
$x^{2}-2x-63=0$\\
$(x-9)(x+7)=0$\\
$x=9,-7$

9

鐔$x$2悵3{̂4ƁCƂ̐$x$ƓȂB
̂ƂC$x$̒l߂B

process
$3x^2-4=x$ \, $3x^2-x-4=0$\\
$(3x-4)(x+1)=0$\\
$x=\displaystyle \frac{4}{3},-1$\\
$x$͐C$x=-1$

$-1$

A̎RC2悵ĉƂ$145$ɂȂB
̂ƂC̐̂̐߂B

process
A鎩R$x$C$x+1$ƂƁC\\
$x^2+(x+1)^2=145$C$x^2+x^2+2x+1=145$C$2x^2+2x-144=0$\\
$x^2+x-72=0$C$(x-8)(x-9)=0$\\
$x=8,9$

$8$

召2̐̐B2̐̍5ŁCς24łB
̂ƂC̐߂B

process
̐$x$ƂƁCӂ傫̐$x+5$ƂB
2̐̐ς24ł邱ƂC\\
$x(x+5)=24$,\,$x^2+5x-24=0$,\,$(x+8)(x-3)=0$
$x>0$ł̂ŁC$x=3$

$3$

$20$kmꂽ2_Ԃ̂ɁCs͗\̑1\,km/hCA͗\̑1\,km/hxŉāC
340B̂ƂC\̑߂B

process
\̑$x$km/hƂƁCs̑$x+1$CȂ$x-1$ƕ\BӂC\\
$\displaystyle \frac{20}{x+1}+\displaystyle \frac{20}{x-1}=3+\displaystyle \frac{40}{60}$\\
$\displaystyle \frac{20}{x+1}+\displaystyle \frac{20}{x-1}=\displaystyle \frac{11}{3}$\\
ӂ$3(x-1)(x+1)$ƁC\\
$60(x-1)+60(x+1)=11(x^2-1)$,\\
$11x^2-120x-11=0$,\,$(11x+1)(x-11)=0$\\
$x>0$ł邩C$x=11$

$11$km/h

A2̎RC
ꂼ2̘áC
Ƃ̎R̘a6{7ɓB
2̎R߂B

process
߂2̎R$x$C$x+1$ƂƁC\\
$x^2+(x+1)^2=6(x+x+1)+7$\\
$2x^2-10x-12=0$\\
$x^2-5x-6=0$\\
$(x-6)(x+1)=0$\\
$x=6$i$\because x \geqq 1$j

$6C7$











[Level5]
Q̖ʐςɊւ镶͑
`̓ynB̓yn̏c̒$1m$C̒$3m$ZĒ`ɂC
ʐς$60cm^{2}$ɂȂB̂ƂCƂ̓yn̈Ђ͉̒$m$B

process
$(x+1)(x-3)=60$\\
$x^{2}-2x-63=0$\\
$(x+7)(x-9)=0$\\
$x=-7,9$

$9m$

`̔B̔̏c̒$1m$C̒$2m$Ē`ɂC
ʐςƂ̔3{ɂȂB̂ƂCƂ̔̈ӂ͉̒$m$B

process
$3x^{2}=(x+1)(x+2)$\\
$2x^{2}-3x-2=0$\\
$(2x+1)(x-2)=0$\\
$x=2,-\displaystyle\frac{~1~}{2}$

2m

̒c̒2{ł钷`B܁C̒`̏c̒$1cm$ZC
̒$4cm$ƂC̒`̖ʐς $36cm^{2}$ ɂȂB
̂ƂCƂ̒`̏c͉̒$cm$H

process
Ƃ̒`̏c̒$x$ƂƁC\\
$(2x+4)(x-1)=36$\\
$2x^2+2x-40=0$
$x^2+x-20=0$\\
$(x+5)(x-4)=0$\\
$x=-5,4$B\\
$x>0$$4cm$

$4cm$

ʐς $27cm^{2}$ łOp`Bӂ̒$3cm$ƂC
$cm$H

process
$x$Ƃ\\
$\displaystyle \frac{1}{2}x(x+3)=27$\\
$x^{2}+3x-54=0$\\
$(x-6)(x+9)=0$\\
$x=6,-9$

$6cm$

ʐς $10cm^{2}$ łOp`B
̎Op`̍Cӂ̒2{$3cm$ZƂCӂ͉̒$cm$H

process
ӂ$x$Ƃ\\
$\displaystyle \frac{1}{2}x(2x-3)=10$\\
$2x^{2}-3x-20=0$\\
$(2x+5)(x-4)=0$\\
$x=4,-\frac{~5~}{2}$

$4cm$

`̏c̒$3cm$C̒$2cm$Ăł钷`̖ʐς$210 cm^{2}$̂ƂC`̂Pӂ̒߂ȂB

process
߂钷$x$ƂƁC$(x+3)(x+2)=210$\\
$x^{2}+5x-204=0$\\
$(x+17)(x-12)=0$\\
$x=-17,12$

$12cm$

`̏c̒$5cm$C̒$2cm$ZĂł钷`̖ʐς$40 cm^{2}$̂ƂC`̂Pӂ̒߂ȂB

process
߂钷$x$ƂƁC$(x-5)(x-2)=40$\\
$x^{2}-7x-30=0$\\
$(x-10)(x+3)=0$\\
$x=10,-3$

$10cm$

c$10cm$`B
̒`̏cQ{ɂC$4cm$ZĂ`̖ʐς$80cm^{2}$ɂȂB
Ƃ̒`̖ʐς߂ȂB

process
Ƃ̒`̏c$=x$C$=x+10$B\\
ό``̏c$=2x$C$=x+6$B\\
$2x(x+6)=80$\\
$x^2+6x-40=0$\\
$(x-4)(x+10)=0$\\
$x=4Bx+10=14$Bʐ$=4 \times 14=56$

$56 cm^2$

̒$60cm$ŁCʐς$216cm^2$ł钷`2ӂ̒߂B

process
2ӂ̒$x,\,y$ƂƁC\\
$x+y=30$c\textcircled{\small 1}\\
$xy=216$c\textcircled{\small 2}\\
\textcircled{\small 1}$y=30-x$c\textcircled{\small 1}'\\
\textcircled{\small 1}'C\textcircled{\small 2}$x(30-x)=216$B$x^2-30x+216=0$\\
$216=2 \times 2 \times 2 \times 3 \times 9$B\\
$(x-12)(x-18)=0$B$x=12,18$

$12cm$$18cm$

`B
܁C`1ӂ$5cm$C1ӂ$5cm$ZƖʐς$600cm^2$̒`ɂȂƂB
̐`1ӂ̒߂B

process
`1ӂ̒$x$ƂƁC\\
$(x+5)(x-5)=600$B$x^2=625$B$x=25$\,($x>0$)

25cm

̒c̒2{ł钷`B
܁C̒`̏c̒$1cm$ZC̒$3cm$ƂC
̒`̖ʐς$18 cm^2$ɂȂB
̂ƂCƂ̒`̏c͉̒$cm$B

process
Ƃ̒`̏c̒$x$ƂƁC\\
$(x-1)(2x+3)=18$C$2x^2+3x-2x-3-18=0$C$2x^2+x-21=0$C
$(2x+7)(x-3)=0$\\
$x=-\displaystyle \frac{7}{2},\, 3$B
$x>0$C$x=3$

$3cm$

`̔B̔̏c̒$1$mC
̒$2$mĒ`ɂC
ʐςƂ̔$3${ɂȂB
̂ƂCƂ̔̈ӂ̒߂B

process
Ƃ̔̈Ђ̒$x$ƂƁC\\
$(x+1)(x+2)=3x^2$,\, $x^2+3x+2=3x^2$\\
$0=2x^2-3x-2$,\, $0=(2x+1)(x-2)$\\
$x=-\displaystyle \frac{1}{2},\, 2$\\
$x$͐̐C$x=2$

$2$m

ӂ̒2{łOp`B̖ʐς$36cm^2$łƂC
ӂ̒߂B

process
ӂ̒$x$ƂƁC$\displaystyle \frac{x}{2}$B
ӂC$\displaystyle \frac{1}{2} \times x \times \displaystyle \frac{x}{2}=36 $B
$x>0$ł̂ŁC$x=12$

$x=12 $ cm

`ƒ`B`̏c͐`1ӂ$5$cmC$6$cmZB
܂C`̖ʐς$42cm^2$łB̂ƂC`1ӂ̒߂B

process
`1ӂ̒$x$ƂƁCӂC\\
$(x-6)(x+5)-42$,\,$x^2-x-72=0$,\\
$(x+8)(x-9)=0$,\, $x=-8,\,9$B\\
$x>0$ł̂ŁC$x=9$

$9$cm

}̂悤2ӂ$16m$C$20m$̒`̓ynB
yn̒ɕ̓HƂCʐςׂ$63m^2$̋悪4łB
H̕߂ȂB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/202_Cs_͑/pic01.tex}
\end{center}

process
H̕$x$ƂƁCӂC\\
$(20-x)(16-x)=4 \times 63$\\
ƁC$x^2-36x+68=0$\\
$(x-2)(x-34)=0,\,x=2,34$\\
$x=34$͕sKB

$2m$

܂̒60m̒`̓ynB
̓ynO㍶EɁCLĖʐς$136m^2$LB
mL΂悢łB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/202_Cs_͑/pic02.tex}
\end{center}

process
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/202_Cs_͑/pic02p.tex}
\end{center}
Ƃ̒`̉̒$x$Cc̒$y$C߂镝$k$ƂƁCӂ\\
$x+y=30$c\textcircled{\small 1}\\
$(x+2k)(y+2k)-xy=136$c\textcircled{\small 2}\\
\textcircled{\small 1}C\textcircled{\small 2}C$k^2+15k-34=0$\\
$(k+17)(k-2)=0$\,$k=2$

$2$m

}̂悤Ȍ𗼑瓯Ő܂Cfʐς$80 \rm cm^2$ɂB
牽cm̂ƂŐ܂Ƃ悢łB
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/202_Cs_͑/pic03.tex}
\end{center}

process
߂钷$x\,$cmƂƁC\\
$x(26-2x)=80$\\
$x^2-13x+40=0$C$(x-5)(x-8)=0$C
$x=5,\,8$

5cmC8cm

c18mC12m̓ynɁC}̂悤ɏcC
ɓ̒ʘHāC
cԂɂB
Ԃ̖ʐς${\rm 160 m^2}$ɂȂ悤ɂɂ́C
ʘH̕mɂ΂悢B
\begin{center}
\input{D:/texlive/2018/bin/win32/mathtex/202_Cs_͑/fig76.tex}
\end{center}

process
ʘH̕$x$mƂƁC\\
$(12-x)(18-x)=160$\\
$(x-12)(x-18)=160$\\
$x^2-30x+56=0$\\
$(x-28)(x-2)=0 \therefore x=2,28$\\
ʘH͉̒̕Ẑ$x=2$

2m

c$6 cm$`B
`̖ʐς$40 cm^2$̂ƂCc̒߂B

process
c̒$x$ƂƁC\\
$x(x+6)=40$\\
$x^2+6x-40=0$\\
$(x+10)(x-4)=0$\\
$x>0$$x=4$

$4cm$

c$8 cm$`B
`̖ʐς$20 cm^2$̂ƂCc̒߂B

process
c̒$x$ƂƁC\\
$x(x+8)=20$\\
$x^2+8x-20=0$\\
$(x+10)(x-2)=0$\\
$x>0$$x=2$

$2cm$

ӂ3cmOp`Cʐς$27 {\rm cm}^2$
łB̎Op`̒ӂ̒߂B

process
ӂ̒$x$ƂB
ӂC\\
$27=\displaystyle\frac{1}{2} x(x+3)$\\
$x^2+3x-54=(x+9)(x-6)=0$\\
$x>0$ł邩$x=6$

$6$








[Level6]
A͑̕i{j
1120~̃m[gA1180~̃m[gB킹9C1,320~͂B
m[gAƃm[gBꂼꉽB

process
A$x$CB$y$Ƃ\\
$x+y=9$@c\textcircled{\small 1}\\
$120x+180y=1320$B$12x+18y=132$@c\textcircled{\small 2}\\
\textcircled{\small 1} $\times-12$:\,$-12x-12y=-108$c\textcircled{\small 1}'\\
\textcircled{\small 2}+\textcircled{\small 1}':\,$6y=24$\,$y=4$\\

A5CB4

150~݂̂ƁC180~̂Ȃ킹10đ680~𕥂B
ꂼꉽB

process
݂$x$CȂ$y$Ƃ\\
$x+y=10$@c\textcircled{\small 1}\\
$50x+80y=680$B$5x+8y=68$@c\textcircled{\small 2}\\
\textcircled{\small 1} $\times-5$:\,$-5x-5y=-50$c\textcircled{\small 1}'\\
\textcircled{\small 2}+\textcircled{\small 1}':\,$3y=18$\,$y=6$\\

݂4CȂ6

M4{ƃm[g3̑680~CM3{ƃm[g6̑960~łB
M1{Cm[g1͂ꂼꂢ炩B

process
M̉i$x$Cm[g̉i$y$Ƃ\\
$4x+3y=680$@c\textcircled{\small 1}\\
$3x+6y=960$@c\textcircled{\small 2}\\
\textcircled{\small 1} $\times-2$:\,$-8x-6y=-1360$c\textcircled{\small 1}'\\
\textcircled{\small 1}'+\textcircled{\small 2}:\,$-5x=-400$\,$x=80$~\\
㎮\textcircled{\small 1}ɑāC$y=120$~

M$80$~Cm[g$120$~

ACB2ނ̏iB
A2B4ł420~CA4B6ł680~łB
A͂炩B

process
Ải$x$CB̉i$y$ƂƁC\\
$2x+4y=420$c\textcircled{\small 1}\\
$4x+6y=680$c\textcircled{\small 2}\\
\textcircled{\small 1}$\times 2:\,4x+8y=840$c\textcircled{\small 1}'\\
\textcircled{\small 2}$\times (-1):\,-4x-6y=-680$c\textcircled{\small 2}'\\
\textcircled{\small 1}'+\textcircled{\small 2}'$2y=160$B$y=80$B\\
㎮\textcircled{\small 1}ɑāC$x=50$

50~

1120~̂Ȃ1180~̂񂲂B1600~ŁĈȂƂ񂲂킹10āCÂ߂ɂB
160~ƂBȂƂ񂲂̌߂B

process
Ȃ̌$x$C񂲂̌$y$ƂƁC\\
$120x+180y+160=1600$\\
$12x+18y=144$c\textcircled{\small 1}\\
$x+y=10$c\textcircled{\small 2}\\
\textcircled{\small 2}$\times (-12):\,-12x-12y=-120$c\textcircled{\small 2}'\\
\textcircled{\small 1}+\textcircled{\small 2}':\, $6y=24$B$y=4$B\textcircled{\small 2}ɑāC$x=6$

Ȃ6C񂲂4

2000~ăW[X𔃂ɍsƂCт12{Əт8{𔃂80~sC
т8{Əт12{𔃂80~]邱Ƃ킩B
̃W[X̑т1{Cт1{̒li͂ꂼꂢ炩B

process
т$x$~Cт$y$~ƂƁC\\
$12x+8y=2080$B$3x+2y=520$c\textcircled{\small 1}\\
$18x+12y=1920$B$2x+3y=480$c\textcircled{\small 2}\\
\textcircled{\small 1}$\times 3:9x+6y=1560$c\textcircled{\small 1}'\\
\textcircled{\small 2}$\times(-2): -4x-6y=-960$c\textcircled{\small 2}'\\
\textcircled{\small 1}'+\textcircled{\small 2}':\,$5x=600$B$x=120$B\textcircled{\small 1}ɑ$y=80$

т120~Cт80~

KXЂ̃KXgṕCKX̎gpʂɉāi{j+iKX$1m^3$̉ij$\times$
iKX̎gpʁjŌvZBKX̎gpʂ$6m^3$̂Ƃ̗́C$1340$~łCKX̎gpʂ
$10m^3$̂Ƃ̗́C1780~łB
KX̎gpʂ$12 m^3$̂Ƃ̗߂B

process
{$x$~C$1m^3$̒P$y$~ƂƁC\\
$x+6y=1340$c\textcircled{\small 1}\\
$x+10y=1780$c\textcircled{\small 2}\\
\textcircled{\small 2}$-$\textcircled{\small 1}:\,$4y=440$B$y=110$~B\textcircled{\small 2}ɑāC$x=680$~B\\
āC$12 m^3$̂Ƃ̗́C\\
$680+12 \times 110=2000$

2000~

pق̓ٗ́Cl300~Cl100~łBِ̓l320lŁCٗ̑z74,000~łB
lƏlِ̓l͂ꂼꉽlB

process
l$x$lCl$y$lCقƂƁCӂC\\
$\left\{ 
\begin{array}{l}
x+y=320 \\
300x+100y=74000
\end{array} \right.$\\
$(1) \times(-100):-100x-100y=32000$\\
$(2):300x+100y=74000$

$x=210,y=110$

Z2l6,000~̕i𔃂߂ɁCZ͏$\displaystyle \frac{1}{2}$C͏$\displaystyle \frac{2}{5}$
oBc̋zׂCZ̕500~BZ̏߂̏͂炩B

process
Z̏$x$~C̏߂̏$y$~ƂƁCӂC\\
$\left\{ 
\begin{array}{l}
\displaystyle \frac{1}{2}x+\displaystyle \frac{2}{5}y=6000 \\
\displaystyle \frac{1}{2}x-\displaystyle \frac{3}{5}y=500
\end{array} \right.$\\
$(1) :\displaystyle \frac{1}{2}x+\displaystyle \frac{2}{5}y=6000$\\
$(2) \times (-1):-\displaystyle \frac{1}{2}x+\displaystyle \frac{3}{5}y=-500$\\
$ y=5500$

$x=7,600$~

Ђ̎Ј171lłB
Ēj40Ə50dԒʋ΂ĂC̐l͓B
̉Ђ̏̎Ј߂B

process
j̐l$x$lC̐l$y$lƂƁC\\
$x+y=171$\,c\textcircled{\small 1}\\
$0.4x=0.5y$\,c\textcircled{\small 2}\\
āC\\
$-4x-4y=-4\times 171$\,c\textcircled{\small 1}$'$\\
$4x=5y$\,c\textcircled{\small 2}$'$\\
\textcircled{\small 1}$'+$\textcircled{\small 2}$':\,-4y=5y-4\times 171$C$y=76$

76l

N͐VЈ150l̗pCN6lB
Njq10Cq20B
N̒jqCq͂ꂼꉽl̗p܂B

process
$N̒jqxCqy$ƂƁC\\
NF$x+y=150$\,c\textcircled{\small 1}\\
NF$0.9x+1.2y=156$\,c\textcircled{\small 2}\\
āC\\
$-9x-9y=-9 \times 150$c\textcircled{\small 1}$'$\\
$9x+12y=1560$c\textcircled{\small 2}$'$\\
\textcircled{\small 1}$'+$\textcircled{\small 2}$'$F$3y=210$C$y=70$B\\
$1.2y=84$lB$0.9x=156-84=72l$

jq72lCq84l









[Level7]
A͑̕ipj
ACB2ނ̍B
A͓60\%ƈ30\%ӂ݁CB͓50\%ƈ45\%ӂłB
2ނ̍āC4\,kgƈ3\,kgӂލɂ́CACBꂼꉽkg΂悢B

process
A$a$\,kgCB$b$\,kgƂƁC\\
$0.60a+0.50b=4$\,c\textcircled{\small 1}\\
$0.30a+0.45b=3$\,c\textcircled{\small 2}\\
\textcircled{\small 2}$\times(-1)$:\,$-0.60a-0.90b=-6$c\textcircled{\small 2}'\\
\textcircled{\small 1}+\textcircled{\small 2}':\,$-0.40b=-2$B$b=5$\\
㎮\textcircled{\small 1}ɑāC$a=2.5$

A2.5kgCB5kg

ACB2ނ̐H킹āC600g̐H肽B
A400gCB200g12\%ɂȂCA150gCB450g7\%ɂȂB
ꂼ̔Zx߂B

process
A̔Zx$x\, \%$CB̔Zx$y\, \%$ƂƁC\\
$400 \times \displaystyle \frac{x}{100}+200 \times \displaystyle \frac{y}{100}=600 \times \displaystyle \frac{12}{100}$\\
$4x+2y=72$c\textcircled{\small 1}\\
$150 \times \displaystyle \frac{x}{100}+450 \times \displaystyle \frac{y}{100}=600 \times \displaystyle \frac{7}{100}$\\
$x+3y=28$c\textcircled{\small 2}\\
\textcircled{\small 2}$\times (-4):\, -4x-12y=-112$c\textcircled{\small 2}'B\\
\textcircled{\small 1}+\textcircled{\small 2}'C$y=4$B\textcircled{\small 2}ɑāC$x=16$

A̔Zx16\%CB̔Zx4\%

ACB2ނ̍B
A͓20\%܂݁CB͓35\%܂łB
ACB̍ē30\%܂ލ120gɂ́CACBꂼꉽg΂悢B

process
A$x$\,kgCB$y$\,kgƂƁC\\
$\displaystyle \frac{20}{100} x+ \displaystyle \frac{35}{100} y=120 \times \displaystyle \frac{30}{100}$\\
$20x+35y=3600$c\textcircled{\small 1}\\
$x+y=120$c\textcircled{\small 2}\\
\textcircled{\small 2} $\times (-20):-20x-20y=-2400$c\textcircled{\small 2}'\\
\textcircled{\small 1}+\textcircled{\small 2}':$15y=1200$B$y=80$B\textcircled{\small 2}ɑāC$x=40$

A40gCB80g







[EOF]

