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I came across a problem about proportion as follow:

There are 5 girls for every 12 boys, if the total number of children is 5200, how many are boys and girls?

I tried following solution but the answer result to decimal number. Since this is number of children, so I believe it should be whole numbers. But I could not come up with the answer of whole number. :( Please help.

Girls = 5/17 X 5200 = 1529.41
Boys = 12/17 X 5200 = 3670.59

Thanks in advance.

sprenna
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    The reasoning is correct: if you subdivide the children in groups of 17 children each, with 5 girls and 12 boys, there should be no remainder. But 5200 is not divisible by 17, so who wrote the problem made a mistake. Maybe they wanted to write 5202. Or two children got lost: go and look for them! ;-) – egreg Sep 10 '13 at 14:26
  • hehe...maybe ;) Thanks for the comment, will verify the problem with my friend. ^_^ – sprenna Sep 10 '13 at 14:30

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Your reasoning is correct: if you subdivide the children in groups of $17$ each, $5$ girls and $12$ boys, there should be no remainder. Then you just multiply the number of groups by $5$ to know the number of girls. It's easier to do the subtraction than multiplying by $12$ to know the number of boys, but the result will be obviously the same.

However, $5200$ is not divisible by $17$, so who wrote the problem made a mistake. Maybe they wanted to write $5202$.

Another possibility is that two children got lost: go and look for them! ;-)

egreg
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