[Title]
203_vZEvZ

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[Problem]
̖₢ɓB

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5

[Level1]
vZ̊{i艿ƌj
$1500~$̏i3̗vŒ艿B艿͂炩B

process
$艿=\times (1+v) $\\
$艿=1500\times (1+0.3)=1950~$

$1950~$

$1000~$̏i3̗vŒ艿B艿͂炩B

process
$艿=\times (1+v) $\\
$艿=1000\times (1+0.3)=1300~$

$1300~$

$500~$̏i3̗vŒ艿B̏i̒艿͂炩B

process
$艿=\times (1+v) $\\
$艿=500\times (1+0.3)=650~$

650~

i艿̂R4200~ŔB̕i̒艿͂炩B

process
$=艿\times (1-)$ \\
$4200=艿\times (1-0.3) $\\
艿=6000~

6000~

i艿̂R3500~ŔB̕i̒艿͂炩B

process
$=艿\times (1-) $\\
$3500=艿\times (1-0.3) $\\
艿=5000~

5000~

ǐ15̗v1840~̒艿B̕ǐ͂炩B

process
$艿1840=\times (1+0.15)$ \\
$= \displaystyle\frac{1840}{1.15}$

1600~

ǐ2̗v1440~̒艿B̕ǐ͂炩B

process
$艿1440=\times (1+0.2) $\\
$= \displaystyle\frac{1440}{1.2}$

1200~

鏤i2̗v7200~̒艿B̏ǐ͂炩B

process
${7200=x\times (1+0.2)=x\times \displaystyle\frac{12}{10}} $\\
$x=7200\times \displaystyle\frac{10}{12}=6000$

6000~

鏤i2̗v8400~̒艿B̏ǐ͂炩B

process
${8400=x\times (1+0.2)=x\times \displaystyle\frac{12}{10}} $\\
$x=8400\times \displaystyle\frac{10}{12}=7000$

7000~

250~̕i2̗vŒ艿B
̕i̒艿͂炩B

process
$250\times(1+0.2)=250\times 1.2=300$

300~

鏤iɌ3̗v悤ɁC艿5200~ɂB͂炩B

process
$x$Ƃ \\
$5200=x\times(1+0.3)=x \displaystyle\frac{13}{10}$

4000~

900~2͂łH

process
$900 \times (1+0.2)=900 \times 1.2=1080$

1080~

$7500$~3͂ɂȂ邩B

process
$7500\times (1-0.3)=7500\times 0.7=5250$~

$5250$~






[Level2]
vZ̊{ilƒ艿j
鏤i艿3Ŕ280~xB̏i̒艿߂ȂB

process
$280=x \times (1-0.3)=x \times 0.7$

400~

艿1200~̏i2ŔƂɂȂ܂H

process
$l=1200\times(1-0.2)=1200 \times 0.8\\
=1200 \times \displaystyle \frac{8}{10}=960$

960~

艿1400~̏i3ŔƂɂȂ܂B

process
$1400\times(1-0.3)=1400 \times 0.7=1400 \times \displaystyle \frac{7}{10}=140 \times 7$

980~

艿1600~̏i2ŔƂɂȂ܂H

process
$l=1600\times(1-0.2)=1600 \times 0.8\\
=1600 \times \displaystyle \frac{8}{10}=1280$

1280~

鏤i艿2Ŕ640~xB
̏i̒艿߂ȂB

process
$l=艿 \times (1-)$\\
$640=x\times(1-0.2)$B$640=x \times 0.8=x \times \displaystyle \frac{8}{10}B$\\
$x=640 \times \displaystyle \frac{10}{8}=800$

800~

3̗vŒ艿i500~lĂ1̗vƂȂB̕ǐ߂ȂB

process
$x$ƂƁC\\
$(1.3x-500)-x=0.1x$

2500~








[Level3]
vZ̉p
ǐ800~łB̕i2̗vŒ艿CȂ̂1Ŕ邱ƂɂB͂炩B

process
$艿=\times (1+v) $\\
$艿=800\times (1+0.2)=960~$ \\
$=艿\times (1-) $\\
$艿=960\times (1-0.1)=864$

864~

25̗v1500~̒艿B͂炩B

process
$x$ƂB \\
$艿=\times (1+v)$ \\
$1500=x\times (1+0.25) $\\
$\displaystyle\frac{1500}{1.25} =1500\times \displaystyle\frac{100}{125}$

1200~

4000~̕iɁC35̗vŒ艿CȂ̂Œ艿2ŔB͂炩B

process
$艿=\times (1+v) $\\
$=艿\times (1-) $\\
$艿=4000\times (1+0.35)$ \\
$=4000\times (1+0.35)\times (1-0.2)=4320~$

4320~

1200~̏i3̗v悤ɒ艿CZ[1ŔB͂炩B

process
$艿=1200\times (1+0.3)=1200 \times\displaystyle\frac{13}{10} $\\
$=1200 \times\displaystyle\frac{13}{10}\times(1-0.1)$

1404~

5000~̏i3̗vŒ艿CȂ̂2ŔB̂Ƃ̔̔i͂炩B

process
$艿=5000\times (1+0.3)=5000+1500=6500 $\\
$=6500\times (1-0.2)=6500-1300=5200$

5200

12.5\%̗v񂾂艿900~ɂȂB
͂炩B

process
$900=x \times (1+1.125)$C$x=\displaystyle\frac{900}{1.125}=800$

800~

25̗vŒ艿C
v500~ƂȂB
艿͂炩B

process
$艿y=x\times (1+0.25)$C\\
$v500=x \times 0.25$C$x=2000$~C\\
$艿=+v=2000+500=2500~$

2500~

600~Ŏdꂽi3̗vŒ艿C
Ȃ̂Œ艿2ɂĔB
v͂炩B

process
$艿=600\times 1.3$C\\
$l=(600\times 1.3)\times (1-0.2)=600\times 1.04=624$C\\
$v=l-=624-600=24$

24~

2̗vŒ艿C
Ȃ̂Œ艿1ɂĔCv100~B
͂炩B

process
$x$ƂƁC\\
艿$=x \times 1.2$\\
l$=(x \times 1.2)\times 0.9=x \times 1.08$\\
v$=x\times 1.08-x$C
$100=x\times 0.08$\\
$x=\displaystyle\frac{100}{0.08}=1250$

1250~

鏤iɌ2݂Œ艿CȂ̂ŁC
艿10\% ɂ800~̗vƂȂB
̌߂B

process
$x$ƂƁC
$1.2x-x=800$

$10,000$~

艿6,000~̕i30\% ŔĂCȂ20\% ̗vB߂B

process
$x$ƂƁCl$=6000\times 0.7$\\
$6000\times 0.7-x=0.20x$

3,500~

鏤i2̗vŒ艿C
Ȃ̂Œ艿2Ŕ100~B
̏ǐ߂ȂB

process
$x$ƂƁC\\
艿$=x(1+0.2)=1.2x$\\
l$=1.2x(1-0.2)=1.2\times 0.8x$\\
$1.2\times 0.8 x-x=-100$\\
$x=\displaystyle\frac{100}{0.4}=2500$

2,500~






[Level4]
vZ̓
鏤i艿3ŔCł5\%Ƃ4410~ɂȂ܂B
̏i̒艿͂łB

process
łƁC$4410 \div 1.05=4200~$B
4200~0.7ɂ̂ŁC艿$4200~ \div 0.7=6000~$

6000~

g}g100Cdl5̒艿C
̂10cCv1750~ƂȂB
g}g1̎dl͂炩B

process
dl$x$~ƂƁC艿$1.5x$~B
ӂC\\
$\displaystyle\frac{3}{2} \times 90x-100x=1750$\\
$135x-100x=1750$C$x=50$

50~

艿2500~̏iCȂ̂2000~Ŕ邱ƂɂB͂炩B

process
$z=2500-2000=500$  \\
$\displaystyle\frac{500}{2500}= \displaystyle\frac{20}{100} $ \\
iʁj \\
$2000=2500(1-x)$

2

鏤ǐ4̗v悤ɒ艿CĉŁC15\%ŔƂ988~̗vB
̏ǐ͂炩B

process
1000~ƂƁC \\
$艿=1000\times (1+0.4)=1400$ \\
$=1400\times (1-0.15)=1400\times \displaystyle\frac{85}{100}=1190$ \\
$v=1190-1000=190 $\\
$x$̂Ƃv988ƂƁC$\displaystyle\frac{1000}{190}= \displaystyle\frac{x}{988}$ \\
$x=988\times \displaystyle\frac{1000}{190} =5200$ \\
iʁj
$x$ƂƁC艿 \\
$艿=x\times (1+0.4)=x \displaystyle\frac{14}{10}$ \\
$=x \times\displaystyle\frac{14}{10}\times (1-0.15)=x \times\displaystyle\frac{14}{10} \times\displaystyle\frac{85}{100}$ \\
$v=988=x \times\displaystyle\frac{14}{10} \times\displaystyle\frac{85}{100}-x= \displaystyle\frac{190}{1000}x$

5200~










[Level5]
vZ̊{
v̒j́C1ԂɉxB

process
j1ԁi60jłЂƉi360ĵŁC\\
$360 \div 60=6$

$6$

v̒Zj́C1ԂɉxB

process
Zj1ԁi60j$360\div 12=30$̂ŁC1Ԃł́C\\
$30\div 60=0.5$

$0.5$

v̒jƒZj́C1Ԃɉx߂Âi܂͗邩jB

process
1ԂɒZj0.5Cj6B
jZjǂĂƂ݂΁C1Ԃ$6-0.5=5.5$߂ÂB
jZj痣ĂƂ݂΁Cl$6-0.5=5.5$ĂB

$5.5$

v̒ZjƒjdȂĂCĂяdȂ͉̂ォB

process
1ԂɒZj0.5Cj6B
jƒZj1Ԃ$6-0.5=5.5$ĂB
360Ă钷jĂяdȂ̂C\\
$360\div 5.5=\displaystyle \frac{360}{5.5}=\displaystyle \frac{720}{11}=65\displaystyle \frac{5}{11}$

$65\displaystyle \frac{5}{11}$

3Ԃ玞v̒jZjɏdȂ܂ł̎Ԃ͉ォB

process
1ԂɒZj0.5Cj6B
jZjǂĂƂC1Ԃ$6-0.5=5.5$߂ÂB
3̂Ƃ͒jƒZj90ĂB
āCdȂ܂ł̎Ԃ́C\\
$90\div 5.5= \displaystyle \frac{90}{5.5}= \displaystyle \frac{180}{11}=16 \displaystyle \frac{4}{11}$

$16 \displaystyle \frac{4}{11}$






[Level6]
vZ̉p
2Ԃ3̊ԂŁCjƒZjΕɈ꒼ɂȂ̂͂łB

process
߂鎞2$t$ƂB
܂C12̈ʒu$0$ƂƁC$2$̈ʒu$360\times \displaystyle \frac{2}{12}=60$\\
$60+0.5t+180=6t$\\
$t=\displaystyle \frac{240}{5.5}=\displaystyle \frac{480}{11}=43\displaystyle \frac{7}{11}$\\
$\displaystyle \frac{7}{11}=\displaystyle \frac{7\times 60}{11}b=\displaystyle \frac{420}{11}b
=38\displaystyle \frac{2}{11}b$

$44338\displaystyle \frac{2}{11}b$

4Ԃ5̊ԂŁCjƒZjΕɈ꒼ɂȂ̂͂łB

process
߂鎞4$t$ƂB
܂C12̈ʒu$0$ƂƁC$4$̈ʒu$360\times \displaystyle \frac{4}{12}=120$\\
$120+0.5t+180=6t$\\
$t=\displaystyle \frac{300}{5.5}=\displaystyle \frac{600}{11}=54\displaystyle \frac{6}{11}$\\
$\displaystyle \frac{6}{11}=\displaystyle \frac{6\times 60}{11}b=32\displaystyle \frac{8}{11}b$

$45432\displaystyle \frac{8}{11}b$

4Ԃ5̊ԂŁCjƒZjpɂȂ̂͂łB

process
߂鎞4$t$ƂB
܂C12̈ʒu$0$ƂƁC$4$̈ʒu$360\times \displaystyle \frac{4}{12}=120$\\
$120+0.5t\pm 90=6t$\\
$t=\displaystyle \frac{210}{5.5}=\displaystyle \frac{420}{11}=38\displaystyle \frac{2}{11}
=38\displaystyle \frac{2\times 60}{11}b=3810\displaystyle \frac{10}{11}b$\\C܂C
$t=\displaystyle \frac{30}{5.5}=\displaystyle \frac{60}{11}=5\displaystyle \frac{5}{11}
=5\displaystyle \frac{5\times 60}{11}b=527\displaystyle \frac{3}{11}b$\\

$4527\displaystyle \frac{3}{11}bC43810\displaystyle \frac{10}{11}b$






[Level7]


[EOF]

