%uemathv𗘗pĂ܂̂ŁCo͂̂Ɂu\bunsuuvgĂ܂B
%̊ɍ킹āCĂB
[Title]
ꎟ͖̕

[Problem]
̖ɓB

[FontSize]
5

[Level1]
Ƒ
150~̂񂲂ƁC130~̂Ȃ킹12C520~xB
ꂼꉽB

process
S̐xƂ\\
50x+30(12-x)=520\\
x=8\\

S@8@Ȃ@4

100~̔ɁC150~݂̂ƁC180~̂񂲂킹15C
傤1000~ɂBꂼꉽꂽ炢B

process
݂̐xƂ\\
100+50x+80(15-x)=1000\\
x=10\\

݂@10@񂲁@5

1100~̂񂲂ƁC1150~̂Ȃ킹15߂Ă炢C
2000~o150~̂肪BꂼꉽB

process
񂲂xƂ\\
100x+150(15-x)=2000-150\\
x=8\\

񂲁@8@Ȃ@7

150~̃`R[gƁC130~̃LfB킹12C
傤500~ɂȂ\ŔɍsBۂɂ́C120~̃v
1߂ɁC`R[ǧ2ȂȂCz\20~ȂB
`R[gƃLfBꂼꉽB

process
ۂɔ`R[gxƂ\\
50x+30(10-x)+120=520\\
x=5\\

`R[g@5@LfB@5

1120~̂񂲉ƁC150~݂̂āC
1100~ɂȂ悤ɂB
݂̌񂲂̌2{ɂ邽߂ɂ́Cꂼꉽ΂悢B

process
񂲂xƂ\\
120x+50\times2x=1100\\
x=5\\

񂲁@5@݂@10

3m̐jgĒ`낤ƎvB
̒Ă̒30cmƁCāEꂼꉽcmɂȂ邩B

process
Ă̒xcmƂ\\
x+x+30=150\\
x=60\\

ā@60cm@@90cm

Z1500~C1200~ĂC2lƂli̖{𔃂̂ŁC
Z̎ĂzC̎Ăz2{ɂȂB{̒li͂炩B

process
{̒lix~Ƃ\\
1500-x=2(1200-x)\\
x=900\\

{̒li@900~

Zƒ͍킹2600~ĂBZ500~̔߂ɁC
Z̎c͒̋z̔ɂȂB2l͍ŏ炸ĂB

process
ZŏɎĂzx~Ƃ\\
2600-x=2(x-500)\\
x=1200\\

Z@1200~@@1400~

[Level2]
֌W
3C4C5 ̂悤ɘA3̐āC̘a264łƂC
3̐߂B

process
^񒆂̐xƂ\\
(x-1)+x+(x+1)=264\\
x=88\\

87C88C89

A4̘̐a426łƂC4̐߂B

process
ŏxƂ\\
x+(x+1)+(x+2)+(x+3)=426\\
x=105\\

105C106C107C108

̈ʂ7ł2̎RB
܁C\̈ʂƈ̈ʂ̐ꂩĂł鐔́CƂ̐18傫ȂB
Ƃ̎R߂B

process
\̈ʂ̐xƂ\\
70+x=10x+7+18\\
x=5\\

57

\̈ʂ6ł2̎RB
܁C\̈ʂƈ̈ʂ̐ꂩĂł鐔́CƂ̐27ȂB
Ƃ̎R߂B

process
̈ʂ̐xƂ\\
10x+6=60+x-27\\
x=3\\

63

̈ʂ̐C\̈ʂ̐2{ł2̎RB
܁C\̈ʂƈ̈ʂ̐ꂩĂł鐔́CƂ̐18傫ȂB
Ƃ̎R߂B

process
\̈ʂ̐xƂ\\
10\times2x+x=10x+2x+18\\
x=2\\

24

\̈ʂ̐ƈ̈ʂ̐Ƃ̘a13ł2̎RB
܁C\̈ʂƈ̈ʂ̐ꂩĂł鐔́CƂ̐27ȂB
Ƃ̎R߂B

process
\̈ʂ̐xƂ\\
10(13-x)+x=10x+(13-x)-27\\
x=8\\

85

A3̋B̘a72̂ƂC3̐߂B

process
^񒆂̋xƂ\\
(x-2)+x+(x+2)=72\\
x=24\\

22C24C26

7C8C912C15C18Ȃǂ̂悤ɂKɂĘAĂ3̐ł́C
ŏ̐ƍő̘̐áCK^񒆂̐2{ɂȂĂB
܁CKɂĘAĂ3̐C3̘̐a
111ŁCŏ̐35łƂCő̐߂B

process
^񒆂̐xƂ\\
x+2x=111\\
x=37\\

39

6 C7 C8 ̂悤ɘA3̐āCԏ5{́Cc2
̘̐aɓƂB3̐߂B

process
^񒆂̐xƂ\\
5(x-1)=x+(x+1)\\
x=2\\

1C2C3

[Level3]
zEW
݂l̎qɕ̂ɁC1l4ɂ16]C
1l5ɂ10ȂȂBq̐lƂ݂̌߂B

process
q̂ɐlxlƂ\\
4x+16=5x-10\\
x=26\\
āČ݂\\
5\times24-10=110\\

l@26l@݂̌@110

炩̂ĉp𔃂ɍsBp15ɂ10~ŝŁC
10Ƃ60~]Bčsz͂炩B

process
p̒lix~Ƃ\\
15x-10=10x+60\\
x=14\\
āCĂz\\
15\times14-10=200~\\

Ăz@200~

َ̉q𔠂ɂ߂̂ɁC112ɂ12]̂ŁC
113ɂ܂5]ƂBَq͑SŉB@@

process
̐xƂ\\
12x+12=13x+5\\
x=7\\
āCَq̐\\
12\times7+12=96\\

َq̐@96

钆wZ̉^LvɍsB1̃eg4lŎg11lȂȂC
5lŎgĂ܂2lȂƂB̉^̃Lvɍsl߂B

process
eg̐xƂ\\
4x+11=5x+2\\
x=9\\
āC̉^̃Lvɍsl\\
4\times9+11=47l\\

l@47l

钆wZ̏CwsŁC̐搶1lɂǂ1SĂ炤ƂɂB
1̔ǂ̐k̐l11lɂƐk8l܂C1̔ǂ̐k̐l12lɂ
k11l̔ǂ4łƂB̐搶̐lƐk̐߂B

process
̐搶̐lxlƂ\\
11x+8=12x-4\\
x=12\\
āCk̐l\\
11\times12+8=140l\\

搶@12l@k@140l

NX̔pW߂̂ɁC1l2500~W߂16000~]C
1l2000~ɂ8000~sBNX̔p͂炩B@

process
lxlƂ\\
2500x-16000=2000x+8000\\
x=48\\
āCNX̔p\\
2000\times48+8000=104000\\

NX̔p@104000~

NXŕW̂ɁCk1l500~W߂2000~sC
600~W߂1600~]B̃NX̕W̂ɕKvȋz͂炩B

process
k̐lxlƂ\\
500x+2000=600x-1600\\
ƁCx=36\\
āCKvȋz\\
500\times36+2000=20000~\\

20000~

钆wZ1NƐ搶7lCoXŎЉȌwɍsB
1̃oX52lƍŌ̃oX21l̍Ȃ܂C
46l3lȂȂƂB
̒wZ1N̐l߂B

process
oX̑䐔xƂ\\
52x-21=46x+3\\
ƁCx=4\\
āC1N̐l\\
52\times4-21-7=180\\

180l

[Level4]
ENȂ
 ݌Z45000~C17500~ĂBCZ3000~C
2500~čsƁCɌZ̒̒2{ɂȂ邩B

process
xɁCZ̒̒2{ɂȂƂ\\
45000+3000x2(17500+2500x)\\
ƁCx=5\\
āC5ƂȂ\\

5

Z640~C230~ĂBZɂnƁC
Z̏͒̏2{ɂȂ邩B

process
Zɓnzx~Ƃ\\
640-x=2(230+x)\\
ƁCx=60\\
āC60~nƂɂȂ\\

60~

AEB\,2̐BAɂ͖3\,\ellCBɂ͖4.5\,\ell ̊ŐꑱĂB
10傤ǂɐ̗̒ʂ͂C
A150\,\ellCB60\,\ell ĂB
A̗̐ʂCB̗̐ʂ2{ɂȂ͉̂B

process
10xƂ\\
150+3x=2(60+4.5x)\\
ƁCx=5\\
āC105ƂȂ

105

镔i̂ɁC1ԂɁCA̋@Bł8CB̋@Bł5邱ƂłB
܂܂łA̋@B104CB̋@B65̕iĂB
ꂩCA̋@B2CB̋@B1ŐYƁC
ȂŠB̑Š3{ɂȂ͉ォB

process
xƂ\\
104+8x\times2=3(65+5x)\\
ƁCx=91\\
āC91ƂȂ\\

91

Y͌10ˁC40˂łB̔NY̔N2{ɂȂ͉̂N̂ƂB

process
xNƂ\\
40+x=2(10+x)\\
ƁCx=20\\
āC20N\\

20N

̔N42˂ŁCq̔N11˂13˂łB̔Nq̔N̘a
2{ł̂͂B

process
xNƂ\\
42+x=2(11+13+2x)\\
ƁCx=-2\\
āC2NOł\\

2NO

[Level5]
̂EE
AEBnԂ̂ɁCs͖60km̓dԂɏC
A͖40km̃oXɏċAƂC140B
AEBԂ̋߂B

process
ABԂ̓̂xkmƂ\\
\bunsuu{x}{60}+\bunsuu{x}{40}=1\bunsuu{2}{3}\\
ƁCx=40\\
āCABԂ40km\\

40km

nCLOA܂ōsBo͎3kmŁC͎8kmŕƂC
ɂԂ245łBA܂ł̋߂B

process
A܂ł̓̂xkmƂ\\
\bunsuu{x}{3}+\bunsuu{x}{8}=2\bunsuu{3}{4}\\
ƁCx=6\\
āCA܂ł̋6km\\

6km

AEBnԂ̂ɁCs͖60mŕCA͖240mőƂC
1ԂBAEBԂ͉̋mB

process
ABԂ̓̂xmƂ\\
\bunsuu{x}{60}+\bunsuu{x}{240}=60\\
ƁCx=2880\\
āCABԂ2880m\\

2880m

ΌNwɌďoĂ10ɁCnN͖ΌN̖Yꕨ͂悤
ƒǂBΌN̑𕪑80mCnN̑𕪑240mƂC
nNoĂΌNɒǂ܂ł̎Ԃ߂B

process
nNoĂ̎ԂxƂ\\
240x=80(10+x)\\
ƁCx=5\\
āC5ɒǂ\\

5

NoĂ15ɁC͍N̖YꕨɋCCԂŌǂB
N̕𕪑75mC̎Ԃ̑45kmƂāC
񂪍Nɒǂ̂́CbォB

process
񂪏oĂ̎ԂxƂ\\
750x=75(15+x)\\
ƁCx=\bunsuu{5}{3}\\
\bunsuu{2}{3}\times60=40b\\
āC140bɂ\\

140b

AnBn܂ōŝɁC35km̑ōsƁC\肵Ԃ3xC
40km̑ōsƁC\肵Ԃ3B
AEBԂ͉̓̂kmB

process
ABԂ̓̂x\ kmƂ\\
\bunsuu{x}{35}-\bunsuu{3}{60}=\bunsuu{x}{40}+\bunsuu{3}{60}\\
ƁCx=28\\
āCABԂ28km\\

28km

ߑO7ɉƂłāC4kmŕƗԂ̔Ԏ5ɉwɓ邱ƂɂȂ̂ŁC
15km̎]ԂōsƁCԂ̔Ԏ17OɉwɓƂB
Ԃ̔Ԏ7B

process
Ԃ̔Ԏ7xƂ\\
4\times\bunsuu{x+5}{60}=15\times\bunsuu{x-17}{60}\\
ƁCx=25\\
āC725ƂȂ\\

725

ŃCƂ1800m̋ɂwZ܂Ŏ]ԂŒʂĂB
CN͂̂ƂɉƂoCrŎ]ԂpN̂ŁC
ĊwZւƂCwZɒԂ6xȂB
N̎]Ԃ̂Ƃ̑𖈕200mC𖈕80mƂāC
N̉Ƃ玩]ԂpNn_܂ł̋߂B

process
pNn_܂ł̋xmƂ\\
\bunsuu{x}{200}+\bunsuu{1800-x}{80}=9+6\\
ƁCx=1000\\
āC]ԂpN͉̂Ƃ1000m̂Ƃ\\

1000m

CmN͉ƑŗVnւBVn܂ł70kmC
ʓHƍH𗘗pāC115łƂłB
Hł̕ς̑80kmCʓHł̕ς̑30kmƂāC
H𑖂߂B

process
H𑖂xkmƂ\\
\bunsuu{x}{80}+\bunsuu{70-x}{30}=1\bunsuu14\\
ƁCx=52\\
āCH𑖂52km\\

52km

900m̒r̂܂C_NƉONn_瓯ɌďoB
_N̑𖈕85mCON̑𖈕60mƂāC
_NŏɉONɒǂƂC_N̕߂B

process
_NONǂ܂łɂԂxƂ\\
85x-60x=900\\
ƁCx=36\\
āC_N̂́̕C85\times36=3060m\\

3060m

120m̗Ԃ90kmőĂB
̗Ԃ̍őOgl̓ɂĂ,
gl𔲂܂140bBgl̒߂B

process
gl̒xmƂ\\
25\times100=x+120\\
ƁCx=2380\\
āCgl̒2380m\\

2380m

230m̉ݕԂCglʉ߂̂240bC
gl}Ԃ132bŒʉ߂B
ݕԂ̑b15mC}Ԃ̑b25m̂ƂC
̓}Ԃ̒߂B

process
}Ԃ̒xmƂ\\
25\times92-x=15\times160-230\\
ƁCx=130\\
āC}Ԃ̒130m\\

130m

[Level6]
(lEEH)
钆wZ̍N̐ḱCN5441lɂȂB
̒wZ̋N̐k߂B

process
N̐kxlƂ\\
(1+0.05)x=441\\
ƁCx=420\\
āCN̐k420l\\

420l

钆wZ̍N̐kCN4504lɂȂB
̒wZ̋N̐k߂B

process
N̐kxlƂ\\
(1-0.04)x=504\\
ƁCx=525\\
āCN̐k525l\\

525l

iC艿15Ă̂ŁC340~ŔƂłB
̕i̒艿͂炩B

process
i̒艿x~Ƃ\\
(1-0.15)x=340\\
ƁCx=400\\
āC̕i̒艿400~\\

400~

i艿25C200~̂ɓĂ2000~
xB̕i1̒艿͂炩B

process
i1̒艿x~Ƃ\\
(1-0.2)x\times5+200=2000\\
ƁCx=450\\
āC̕i1̒艿450~\\

450~

Xł́C2640~ŔĂB̔lɂ͌25̗v܂܂ĂB
̂1̌͂炩B

process
1̌x~Ƃ\\
(1+0.25)x=320\\
ƁCx=256\\
āC1̌256~\\

256~

鏤Xł́CiAɌ4̗v݂Œ艿ĂB
{́CŕiA艿15тŔƂC
1ɂ228~̗vBiǍ߂B

process
iǍx~Ƃ\\
(1+0.4)x\times(1-0.15)=x+228\\
ƁCx=1200\\
āCiǍ1200~\\

1200~

1000~̕iB̕i艿2ŔĂC
120~̗vo悤ɂB艿ɂ΂B

process
i̒艿x~Ƃ\\
(1-0.2)x-1000=120\\
ƁCx=1400\\
āCi̒艿1400~\\

1400~

钆wZ̍N̓wҐ180lłBNx̓wҐ͒jq8C
q5ʁCŜł4lȂȂBNx̒jq̓wҐ߂B

process
N̒jq̓wҐxlƂ\\
x(1-0.08)+(180-x)\times(1+0.05)=436\\
ƁCx=100\\
āCN̒jq̐l\\
100\times0.92=92l\\

92l

钆wZ̍Nx̐ĺCjqq10lB
Nx́Cjq̐l5Cq̐l6̂ŁC
Ŝł2lƂɂȂBNx̒jq̓wҐ߂B

process
Nx̏q̐lxlƂ\\
0.05(x+10)-0.06x=-2\\
ƁCx=250\\
āCNx̒jq̐l\\
260\times1.05=273l\\

273l

6̐H300gBɐ4ɂ߂B
g̐΂B

process
鐅̗ʂx gƂ\\
\bunsuu{4}{100}\times(300+x)=\bunsuu{6}{100}\times300\\
ƁCx=150\\
āC鐅̗ʂ150 g\\

150 g

10̐H400 gBɐH gāC20̔ZɂB
H炢B

process
H̗ʂx gƂ\\
\bunsuu{10}{100}\times400+x=\bunsuu{20}{100}\times(400+x)\\
ƁCx=50\\
āCH̗ʂ50 g\\

50 g

6̐H3̐HāC5̐H300 g肽B
6̐H͉炢B@

process
6̐H̗ʂx gƂ\\
\bunsuu{6}{100}x+\bunsuu{3}{100}\times(300-x)=\bunsuu{5}{100}\times300\\
ƁCx=200\\
āC6̐H̗ʂ200 g\\

6@200 g@@3@100 g

[Level7]
̑
錎̃J_[̐j4񂠂Cׂ̐ĉ62ɂȂB
̌̍Ō̐j͉߂B

process
ŏ̐jxƂ\\
x+(x+7)+(x+14)+(x+21)=62\\
ƁCx=5\\
āC5+21=26\\

26

Xł́CzbgR[q[1t300~CACXR[q[1t400~łB
ōC25̓ɂ́CzbgR[q[160tCACXR[q[30tꂽB
鐔́CōC1オ邲ƂɁCzbgR[q[10tC
ACXR[q[15tB
̔zȂ̂́CōĈƂB

process
ōC25xƂ\\
300(160-10x)=400(30+15x)\\
ƁCx=4\\
āC̔zȂ̂\\
25+4=29̂Ƃ\\

29

100~ʂ𓊂C\o2_Co3_ƂăQ[n߂ƂC
20񓊂ƂCΌN̓_47_ɂȂĂB
ΌN͕\oB

process
 \̏o񐔂xƂ\\
2x+3(20-x)=47\\
ƁCx=13\\

13

CtCǐZ3lŁCRs[^[̃\tgEFA𔃂̂ɁC
͑̔300~oCt͗̏o\bunsuu23oC
i͌t̏o\bunsuu13200~oB
̃\tgEFȂ͂炩B

process
\tgEFȂx~Ƃ\\
\bunsuu12x+200+\bunsuu13x+200+\bunsuu19x+\bunsuu{800}{3}=x\\
ƁCx=13800\\
āC\tg13800~

13800~

钆wZŁCʊwHɎ̂ĂĂ󂫊ʂW߂B
傫̃A~ʂƃX`[ʂ킹1140W܂C
̑dʂ38kgłBA~1̏d20gC
X`[1̏d60ĝƂCA~ʂƃX`[ʂꂼꉽ
W܂B

process
A~ʂ̌xƂ\\
20x+60(1140-x)=38000\\
ƁCx=760\\
āCA~760C\\
XeB[ʂ1140-760=380\\

A~ʁ@760@XeB[ʁ@380

W̓ꗿ́Cl300~Cq150~łB
̓Ґ350lŁCꗿ̍v84000~łBq̓Ґ߂B

process
q̓ҐxlƂ\\
150x+300(350-x)=84000\\
ƁCx=140\\
āCqǂ̓Ґ140l\\

140l

{[Ƃ邽߂̔ꂼꉽB
190ĂƁC17̃{[炸ɎcB
܂̔100{[ĂƁC
Ō1ɂ7ȂB{[͑Sŉ邩B

process
̐xƂ\\
90x+17=100(x-1)+7\\
ƁCx=11\\
āC{[̌\\
90\times11+17=1007\\

1007

NX̏qk22lłB
̃NX̒jqk̓NXŜ̂4lȂƂB
̃NXŜ̐l߂B

process
NX̐lxlƂ\\
x-22=\bunsuu12x-4\\
ƁCx=36\\
āCNXŜ̐l36l\\

36l

[EOF]

