% %ȉ̕RgƂ̂łC_ł͂܂ł܂B
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[Title]
103_dZ

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̖₢ɓB
% tHg̑傫B1`10C܂TeX̃R}hw肷B
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% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
{
d̂ɁCY1lł10ԂCYCY2lł6ԂƂB
̎dY1lłƉԂ邩H

process
߂$x$ƂƁC\\
$\left( \displaystyle \frac{1}{10}+\displaystyle \frac{1}{x} \right)\times 6=1$\\
$\displaystyle \frac{1}{10}+\displaystyle \frac{1}{x}=\displaystyle\frac{1}{6}$

15

鐅ɂ͋ǂƔrǂCpAǂ͐ɐ𖞂̂6ԂC
rpBǂ͐Ă鐅琅ô8Ԃ܂B
2̊ǂSJɂĐ𓯎ɏoꂷƂC܂łɉԂ܂H

process
߂鎞Ԃ$x$ԂƂƁC\\
$\left( \displaystyle \frac{1}{6}-\displaystyle \frac{1}{8} \right)\times x=1$~~~~
$\displaystyle\frac{1}{24}\times x=1$

24

ddグ̂ɊAł120CBł60B
AƊBł̎dɎgނƂC̎ddグ̂ɉ邩H

process
߂$x$ƂƁC\\
$\left( \displaystyle\frac{1}{120}+\displaystyle\frac{1}{60} \right)\times x=1$\\
$\displaystyle\frac{1}{120}+\displaystyle\frac{1}{60}=\displaystyle\frac{1}{x}$

40

鐅tɐ͂ƂCA̎֌Ő15C
B̎֌Ő10܂B̎֌gĐƁC
͉ňtɂȂ܂H

process
̑S̗eς1ƂƁCPʎԂ̎dʁi\́j́C\\
֌Ac$\displaystyle \frac{1}{15}$C֌Bc$\displaystyle \frac{1}{10}$C\\
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle \frac{1}{15}+\displaystyle \frac{1}{10} \right)\times x=1$~~~
$\displaystyle \frac{1}{15}+\displaystyle \frac{1}{10}=\displaystyle\frac{1}{x}$

6ij

鐅ɂ͋ǂƔrǂC
pAǂ͐ɐ𖞂̂3ԂC
rpBǂ͐Ă鐅琅ô4Ԃ܂B
2̐SJɂĐoꂷƂC
܂łɉԂł傤B

process
߂鎞Ԃ$x$ԂƂƁC\\
$\left( \displaystyle\frac{1}{3}-\displaystyle\frac{1}{4} \right)\times x=1$

12

ddグ̂ɁCMN2l30ԂB
Mœ80ԂƂƁCNł͉Ԃ邩B

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle \frac{1}{80}+\displaystyle \frac{1}{x} \right)\times 30=1$\\
$\displaystyle \frac{1}{80}+\displaystyle \frac{1}{x}=\displaystyle \frac{1}{30}$

48

o镔̑|邱ƂɂȂ܂B
̕1lő|ƁCo20C30܂B
2lłɂƉŏI邱Ƃł܂B

process
o1̎dʂ$\displaystyle \frac{1}{20}$C\\
1̎dʂ$\displaystyle \frac{1}{30}$C\\
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle \frac{1}{20}+\displaystyle \frac{1}{30} \right) \times x=1$~~~
$\displaystyle \frac{1}{20}+\displaystyle \frac{1}{30}=\displaystyle\frac{1}{x}$

12

AN1l15CBN1l30Ƃ2lłɂƁC
ŏI܂B

process
1̎dʂ́C\\
Ac$\displaystyle \frac{1}{15}$CBc$\displaystyle \frac{1}{30}$\\
߂$x$ƂƁC\\
$\left( \displaystyle \frac{1}{15}+\displaystyle \frac{1}{30}\right)\times x=1$~~~
$ \displaystyle \frac{1}{15}+\displaystyle \frac{1}{30}=\displaystyle\frac{1}{x}$ 

10

d̂ɁCAN1lł15CANBN2lł6܂B
BN1lł͉܂B

process
߂$x$ƂƁC\\
1̎dʂ́C\\
Ac$\displaystyle \frac{1}{15}$C
Bc$\displaystyle \frac{1}{x}$\\
$\left( \displaystyle \frac{1}{15}+\displaystyle \frac{1}{x} \right)\times 6=1$\\
$\displaystyle \frac{1}{15}+\displaystyle \frac{1}{x}=\displaystyle \frac{1}{6}$

10

v[ɐ̂ACB2̋ǂB
A̋ǂgƃv[30łςɂȂCB̋ǂ45łςɂȂB
ACB2̋ǂ𓯎ɎgƁCŃv[͂ςɂȂ邩B

process
A1Ԃ̎dʂ$\displaystyle \frac{1}{45}$C
B1Ԃ̎dʂ$\displaystyle \frac{1}{30}$B\\
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle \frac{1}{30}+\displaystyle \frac{1}{45}\right)\times x=1 $\\
$\displaystyle \frac{1}{30}+\displaystyle \frac{1}{45}=\displaystyle\frac{1}{x}$~~~
$\displaystyle\frac{3}{90}+\displaystyle\frac{2}{90}=\displaystyle\frac{1}{x}$

18

AN1lł12ԁC
BN1lł6ԂŏIdB
̎dANCBN2lłƉ邩B

process
߂$x$ƂƁC\\
$\left( \displaystyle\frac{1}{12}+\displaystyle\frac{1}{6} \right)\times x=1$\\
$\displaystyle\frac{1}{12}+\displaystyle\frac{1}{6}=\displaystyle\frac{1}{x}$

4

鐅Ɏ֌AgĐ24C
֌Bł12B
֌ACB̗𓯎ɎgƉԂŐ͈tɂȂ邩B

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle\frac{1}{24}+\displaystyle\frac{1}{12} \right)\times x=1$\\
$\displaystyle\frac{1}{24}+\displaystyle\frac{1}{12}=\displaystyle\frac{1}{x}$

8

AN1lł12ԂdB
̎d܂AN4ԂɁC
cBN1lłƂ6B
̎dBN1lłƉԂ邩B

process
߂$x$ƂƁC\\
$\displaystyle\frac{1}{12} \times 4+\displaystyle\frac{1}{x}\times 6=1$\\
$x=9$

9

1lœck20B10kCc𑷂1l30čkIB
1lł1ԂɑŜ̂ǂꂾkƂł邩H

process
1̎dʂ$\displaystyle \frac{1}{20}$B1̎dʂ$x$ƒ߂ƑӂC\\
$\displaystyle \frac{1}{20} \times 10 +x \times 30=1$@$x=\displaystyle \frac{1}{60}$

$\displaystyle \frac{1}{60}$

d̂ɁCAN1lł12CBN1lł15CCN1lł20܂B
̎d3lłƁC܂B

process
߂$x$ƂƁC\\
1̎dʂ\\
ANc$\displaystyle \frac{1}{12}$CBNc$\displaystyle \frac{1}{15}$CCNc$\displaystyle \frac{1}{20}$\\
$\left( \displaystyle \frac{1}{12}+\displaystyle \frac{1}{15}+\displaystyle \frac{1}{20} \right)\times x=1$

5

^gbNȂ12C^16C^ł24̉ו܂B
^Ə^1䂸ƒ^2𓯎ɎgƁCŉ^т邱Ƃł܂B

process
1̉ʂ́C\\
c$\displaystyle \frac{1}{12}$Cc$\displaystyle \frac{1}{16}$C
c$\displaystyle \frac{1}{24}$\\
+2+c\\
$\displaystyle \frac{1}{12}+\displaystyle \frac{1}{16} \times2+\displaystyle \frac{1}{24}
=\displaystyle \frac{2}{24}+\displaystyle \frac{3}{24}+\displaystyle \frac{1}{24}=\displaystyle \frac{6}{24}
=\displaystyle \frac{1}{4}$

4

A񂪂Plł36CAB2lꏏɂ12d܂B̎dB1lłƉ܂B

process
߂$x$ƂƁC\\
$\left( \displaystyle\frac{1}{36}+\displaystyle\frac{1}{x} \right)\times 12=1$\\
$\displaystyle\frac{1}{36}+\displaystyle\frac{1}{x}=\displaystyle\frac{1}{12}$

18

Ƃ̂ɁCclł36ԂKvŁC؂lł72ԂKvłB̍Ƃlɍsꍇɂ͉ԂKvH 

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle\frac{1}{36}+\displaystyle\frac{1}{72} \right)\times x=1$\\
$\displaystyle\frac{1}{36}+\displaystyle\frac{1}{72}=\displaystyle\frac{1}{x}$

24

Ƃ̂ɁCclł6ԂKvŁC؂lł12ԂKvłB̍Ƃlɍsꍇɂ͉ԂKvH

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle\frac{1}{6}+\displaystyle\frac{1}{12} \right)\times x=1$\\
$\displaystyle\frac{1}{6}+\displaystyle\frac{1}{12}=\displaystyle\frac{1}{x}$

4

Ƃ̂ɁCclł12ԂKvŁC؂lł36ԂKvłB̍Ƃlɍsꍇɂ͉ԂKvH 

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle\frac{1}{12}+\displaystyle\frac{1}{36} \right)\times x=1$\\
$\displaystyle\frac{1}{12}+\displaystyle\frac{1}{36}=\displaystyle\frac{1}{x}$

9

Ƃ̂ɁCclł24ԂKvŁC؂lł12ԂKvłB̍Ƃlɍsꍇɂ͉ԂKvH

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle\frac{1}{24}+\displaystyle\frac{1}{12} \right)\times x=1$\\
$\displaystyle\frac{1}{24}+\displaystyle\frac{1}{12}=\displaystyle\frac{1}{x}$

8

A 1lōs10CB 1lōs15ďIdB
̎dAB2lōsƂCI܂łɂ͂炩B

process
߂$x$ƂƁC\\
$\left( \displaystyle\frac{1}{10}+\displaystyle\frac{1}{15} \right)\times x=1$

6

A 1lōs12CAB2lōs8ďIdB
̎dB 1lōsƂCI܂łɂ͂炩B

process
߂$x$ƂƁC\\
$\left( \displaystyle\frac{1}{12}+\displaystyle\frac{1}{x} \right)\times 8=1$\\
$\displaystyle\frac{1}{x}=\displaystyle\frac{1}{8}-\displaystyle\frac{1}{12}=\displaystyle\frac{1}{24}$

24

^gbNȂ6C^ł12̉ו܂B^1Ə^2𓯎ɎgƁCŉ^т邱Ƃł܂B

process
1̉ʂ́C\\c$\displaystyle \frac{1}{6}$C
c$\displaystyle \frac{1}{12}$\\+c\\
$\displaystyle \frac{1}{6}+\displaystyle \frac{1}{12} \times 2=\displaystyle \frac{1}{3}$

3

dI点̂ɁC
A1lł20C
B1lł30B
̎dACB 2lŏI点̂ɁC邩߂ȂB

process
$\displaystyle\frac{1}{20}+\displaystyle\frac{1}{30}=\displaystyle\frac{1}{12}$

12







[Level2]
{
𖞂̂ɁCXǂł12ԁCYǂł15ԂB܂C̐ɂ̂ɁCZǂł20ԂB
C3̊ǂ𓯎ɊJāC̐𖞐ɂɂ͉Ԃ邩H

process
߂鎞Ԃ$x$ƂƁC\\
$\left( \displaystyle \frac{1}{12}+\displaystyle \frac{1}{15}-\displaystyle \frac{1}{20} \right)\times x=1$\\
$\displaystyle \frac{5}{60}+\displaystyle \frac{4}{60}-\displaystyle \frac{3}{60}=\displaystyle \frac{1}{x}$

10

db1lł6C1lł8B
̎dbCC3lł3łނƂB
1lł̎dsƉ邩B

process
߂$x$ƂƁC
1̎dʂ́C\\
bc$\displaystyle \frac{1}{6}$Cc$\displaystyle \frac{1}{8}$C
c$\displaystyle \frac{1}{x}$ \\
$\left( \displaystyle \frac{1}{6}+ \displaystyle \frac{1}{8}+\displaystyle \frac{1}{x} \right) \times 3=1$\\
$\displaystyle \frac{1}{6}+ \displaystyle \frac{1}{8}+\displaystyle \frac{1}{x}=\displaystyle\frac{1}{3}$~~~
$\displaystyle \frac{4}{24}+ \displaystyle \frac{3}{24}+\displaystyle \frac{1}{x}=\displaystyle\frac{8}{24}$

24

^N𖞐ɂ̂ɁC1̃pCvł4ԁC2̃pCvł6ԂƂB
܂C3̃pCv͔rǂŁCr12ԂB
3{̃pCv𓯎ɎgC^N𖞐ɂ̂ɉԂ邩B

process
߂鎞Ԃ$x$ԂƂƁC\\
$\left( \displaystyle \frac{1}{4}+\displaystyle \frac{1}{6}-\displaystyle \frac{1}{12} \right)\times x=1$

3

A1lł8CB1lł12d܂B
̎dC͂2l3ԂČ́CA1lłĊ܂B
A1lł͉̂ԂłB

process
1̎dʂ́C\\
A$\cdots \displaystyle \frac{1}{8}$C
B$\cdots\displaystyle \frac{1}{12}$C\\
AB$\cdots\displaystyle \frac{1}{8}+\displaystyle \frac{1}{12}
=\displaystyle \frac{5}{24}$B\\
߂$x$ƂƁC\\
$\displaystyle \frac{5}{24} \times 3+\displaystyle \frac{1}{8} \times x=1$B$x=3$

3

dA 1lł12ԂCB 1lł15ԂB
̎dA3ԂA B 2lŉԂďIB
ACB 2lł͉̂B

process
1̎dʂ́C\\
A$\cdots \displaystyle\frac{1}{12}$CB$\cdots \displaystyle\frac{1}{15}$\\
߂$x$ƂƁC\\
$\displaystyle \frac{1}{12} \times 3+\left( \displaystyle \frac{1}{12}+\displaystyle \frac{1}{15} \right)
\times x=1$

5






[Level3]
p
j3l8ԂdC4lł7ԂƂB
̎dj2lC7lłƉԂ邩H

process
1̎dʂ́C\\
j1lc$1 \div 3 \div 8=\displaystyle \frac{1}{24}$C\\
1lc$1 \div 4 \div 7=\displaystyle \frac{1}{28}$B\\
߂$x$ƂƁC\\
$\left( \displaystyle \frac{1}{24} \times 2 + \displaystyle \frac{1}{28} \times 7 \right)\times x=1$

3

ddグ̂ɁCAN1lł12CBN1lł24B
܂CANCBNCCN3lꏏɂ̎dƁCdグ̂4B
̎ddグ̂ɁCCN1lł͉邩H

process
߂$x$ƂƁC
1ɂdʂ\\
AN$\cdots\displaystyle\frac{1}{12}$CBN$\cdots\displaystyle\frac{1}{24}$C
CN$\cdots\displaystyle\frac{1}{x}$\\
$\left( \displaystyle \frac{1}{12}+\displaystyle \frac{1}{24}+\displaystyle\frac{1}{x} \right)\times 4=1$

8

q1lł12CDq1lł15d܂B
̎d𐹎qƍDq2l5ԂCc𐹎q1lł܂B
q́Cd͂߂ĂI܂łɁCԓƂɂȂ܂B

process
1̎dʂ́C\\
qc$\displaystyle \frac{1}{12}$~~~
Dqc$\displaystyle \frac{1}{15}$\\
qƍDqc$\displaystyle \frac{1}{12}+\displaystyle \frac{1}{15}
=\displaystyle \frac{9}{60}=\displaystyle \frac{3}{20}$\\
q1lł$x$ƂƁC\\
$\displaystyle \frac{3}{20} \times 5+\displaystyle \frac{1}{12} \times x=1$\\
$\displaystyle \frac{3}{4}+\displaystyle \frac{1}{12} \times x=1$C
$\displaystyle \frac{1}{12} \times x=\displaystyle \frac{1}{4}$\\
$x=3$Bq񂪎d͂߂ĂI܂łɁC5+3=8

8

YN30ŏICԎq񂪂20ŏIdB
̎dCn߂6Ԃ͑YN1lłāCc͑SĉԎq1lłƁCdn܂ĂI܂łɑSŉ邩H

process
dŜ̗ʂ1ƂƁC1̎dʂ\\
YN$\cdots \displaystyle \frac{1}{30}$C
Ԏq$\cdots \displaystyle \frac{1}{20}$\\
Ԏq$x$ƂƁC\\
$\displaystyle \frac{1}{30}\times 6+\displaystyle \frac{1}{20}\times x=1$
$x=16$B߂$6+16=22$

22

ddグ̂ɁCAN1lł16CBN1lł12B
AN4ԎdČCBN6dBcĂd͑Ŝ̂ǂꂾH

process
dŜ̗ʂ1ƂƁC1̎dʂ\\
AN$\cdots \displaystyle \frac{1}{16}$C
BN$\cdots \displaystyle \frac{1}{12}$\\
cĂd$y$ƂƁC\\
$\displaystyle \frac{1}{16}\times 4+\displaystyle \frac{1}{12}\times 6+y=1$~~~
$y=\displaystyle \frac{1}{4}$

$\displaystyle \frac{1}{4} $i41j

ddグ̂AN15CBN10B
̎d2lňꏏɍsƂɂCrBNaC5x񂾁B
̎d̂ɉ邩B

process
߂$x$ƂƁC\\
ꏏɓ
ANœ́i$x-5$jBBN$x$B\\
$\displaystyle\frac{1}{10}\times (x-5)+\displaystyle\frac{1}{15}x=1$\\
$\left(\displaystyle\frac{1}{10}+\displaystyle\frac{1}{15}\right)x=1+\displaystyle\frac{1}{2}$

9

ANd8B܂CBNd12B
ANBNꏏɂ̎dƁCڂŎdI邩H\\
{\bf A} 1,  {\bf B} 2,  {\bf C} 3,  {\bf D} 4\\
{\bf E} 5, {\bf F} 6,  {\bf G} 7,  {\bf H} 8

process
dŜ̗ʂ1ƂƁC1̎dʂ\\
AN$\cdots \displaystyle\frac{1}{8}$CBN$\cdots \displaystyle\frac{1}{12}$\\
߂$x$ƂƁC\\
$ \left( \displaystyle \frac{1}{8}+\displaystyle \frac{1}{12} \right)\times x=1$B
$x=\displaystyle \frac{24}{5}=4.8$B
dÎ5ڂ̓rB

{\bf E} 5

10l12dC15lłƉ܂B

process
1l̎dʂ$\displaystyle\frac{1}{x}$ƂƁC\\
$\displaystyle\frac{1}{x}\times 10 \times 12=1$
$x=120$B\\
߂$y$ƂƁC$\displaystyle \frac{1}{120}\times 15 \times y=1$\\
$y=\displaystyle \frac{120}{15}=\displaystyle \frac{40}{5}=8$

8

鐅𖞂̂Aǂł4ԂCBǂł6Ԃ܂B
ł́CɎgΉԉŐ𖞂Ƃł܂H

process
̗eς1ƂƁC1Ԃ̗̐ʁiʁj\\
Aǂ̂$\cdots \displaystyle \frac{1}{4}$B
Bǂ̂$\cdots \displaystyle \frac{1}{6}$B\\
߂鎞Ԃ$x$ԂƂƁC\\
$\left( \displaystyle \frac{1}{4}+\displaystyle \frac{1}{6} \right)\times x=1$B\\
$x=\displaystyle \frac{12}{5}
=\displaystyle \frac{24}{10}=2.4=2+60 \times \displaystyle \frac{4}{10}=224$

224

悤q1lł40ԁCq1lł60dB
̎d悤qCq2lłɂ͂߂Crłq񂪋x񂾂߂ɁC
dグ̂30ԂBq񂪋x񂾂͉̂ԂH

process
1̎dʂ́C\\
悤qc$\displaystyle \frac{1}{40}$Cqc$\displaystyle \frac{1}{60}$B\\
߂$x$ƂƁC\\
$\left( \displaystyle \frac{1}{40}+\displaystyle \frac{1}{60} \right)\times (30-x)+\displaystyle \frac{1}{40}\times x=1$\\
$\displaystyle \frac{1}{40} \times 30+\displaystyle \frac{1}{60}\times(30-x)=1$\\
$\displaystyle \frac{1}{60}\times(30-x)=\displaystyle \frac{1}{4}$

15

YN1lł9CԎq1lł15d܂B
̎dC͂߂̉𑾘YN1lāČォĉԎq1lłƁC
S11܂B̂ƂCԎq񂪓͉ԂłB

process
1̎dʂ\\
Y$\cdots\displaystyle \frac{1}{9}$C
Ԏq$\cdots\displaystyle \frac{1}{15}$\\
Ԏq$x$ƂƁCӂC\\
$\displaystyle \frac{1}{9}\times  (11-x) +\displaystyle \frac{1}{15}\times x=1$C
$\displaystyle \frac{11}{9} +\left( \displaystyle \frac{1}{15}-\displaystyle \frac{1}{9} \right)x=1$\\
$\displaystyle \frac{11}{9} -1=\left( \displaystyle \frac{1}{9}-\displaystyle \frac{1}{15} \right)x$C
$\displaystyle \frac{2}{9}=\displaystyle \frac{2}{45}x$\\
$x=\displaystyle \frac{2}{9} \div \displaystyle \frac{2}{45}
=\displaystyle \frac{2}{9} \times \displaystyle \frac{45}{2}=5$

5

d̂ɁCAN30CBN20CCN15B
̎dANCBNCCN3lłƂCBNԂx񂾂̂ŁCdÎɂ傤7B
BNx񂾂͉̂H

process
Ŝ̎d̗ʂ1ƂƁC1̎dʂ\\
AN$\cdots\displaystyle \frac{1}{30}$C
BN$\cdots\displaystyle \frac{1}{20}$C
CN$\cdots\displaystyle \frac{1}{15}$\\
BNx񂾓$x$ƂƁCANCCN$7$CBN$7-x$ł邩C\\

$\left( \displaystyle \frac{1}{30}+\displaystyle \frac{1}{15} \right) \times 7+\displaystyle \frac{1}{20}\times (7-x)=1$\\
$x=1$

1

ACB 2l̈̎d̂ɁC
ꂼ1lłA640CB4ԂB
̂ƂCACBꏏɎdƁCԉł̎dI邩B

process
$640=6 \displaystyle \frac{2}{3}=\displaystyle \frac{20}{3}$B\\
߂鎞Ԃ$x$ԂƂƁC\\
$\left( \displaystyle \frac{3}{20}+\displaystyle \frac{1}{4} \right)\times x=1$\\
$x=\displaystyle\frac{20}{8}=$2.5=230

230

𖞂̂ɁCa1{g12ŖɂȂCb1{g16ŖɂȂB
a1{b2{𓯎ɎgƉbŖɂȂ邩H

process
dŜ̗ʂ1ƂƁC1Ԃ̎dʂ́C\\
ac$\displaystyle \frac{1}{12}$Cbc$\displaystyle \frac{1}{16}$B\\
aƁib $\times 2 $j c
$\displaystyle \frac{1}{12}+\displaystyle \frac{1}{16} \times 2=
\displaystyle \frac{1}{12}+\displaystyle \frac{1}{8}=\displaystyle \frac{5}{24}$B\\
߂鎞Ԃ$x$ƂƁC\\
$\displaystyle \frac{5}{24} \times x=1$\\
$x=\displaystyle \frac{24}{5}=4 \,\displaystyle \frac{4}{5}
=4ij60 \times \displaystyle \frac{4}{5}ibj\\
=4ij48ibj$

4ij48ibj

MCN2ނ̃m[gBm[gM18zŃm[gN24B
C̋zŃm[gM12ƎĉŃm[gN邩H

process
m[gM18CN24zŚC1~ƍlƁC\\
M1c$\displaystyle \frac{1}{18}$~CN1c$\displaystyle \frac{1}{24}$~B\\
߂鐔$x$ƂƁC\\
$\displaystyle \frac{1}{18}\times 12+\displaystyle \frac{1}{24}\times x=1$

8

Y1lł12CY1lł18dB
̎d𑾘YƎY2l6ԓCcY1lœB
̎ddグ̂ɁC킹ĉԂ邩H

process
1̎dʂ́C\\
Yc$\displaystyle\frac{1}{12}$C
Yc$\displaystyle\frac{1}{18}$B\\
YƎYc$\displaystyle \frac{1}{12} + \displaystyle \frac{1}{18}=\displaystyle \frac{5}{36}$B\\
Y1lœ$x$ƂƁC\\
$\displaystyle\frac{5}{36} \times 6+\displaystyle\frac{1}{18}\times x=1$\\
$\therefore x=3$B߂$6+3=9$

9






[Level4]

^Nɐ𖞂ƂɁC
ACB\,2̊ǂg15ԂC
Ag20Ԃ܂B
܁CACBgĐn߂ƂrA琅oȂȂ܂B
̌BŐn߂Ƌ̏Ԃ疞ɂȂ܂ł27Ԃ܂B
ACBgĂԂ߂ȂB

process
Aǂ̋$\displaystyle\frac{1}{20}$C
(A+B)̋$\displaystyle\frac{1}{15}$C
Bǂ̋$\displaystyle\frac{1}{15}-\displaystyle\frac{1}{20}=\displaystyle\frac{1}{60}$ƂȂB
ACBgĂԂ$x$ԂƂƁCBgĂԂ$(27-x)$ԂC\\
$\displaystyle\frac{1}{15} x+\displaystyle\frac{1}{60} (27-x)=1$\\
$4x+(27-x)=60$C$x=11$

11






[Level5]



[Level6]


[Level7]


[Level8]




[EOF]

