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Im working on ratios for GCSE, I've become comfortable increasing/decreasing ratios and sharing values based on ratios but Im not sure how to proceed with this type of question.

Intially I thought along the lines of 10/14 to calculate the amount of 'foods' for each child. Then multiple that by 3 to get the value of food for the boys that dont come and add that to the 14 however, my materials tell me the answer should be 20days. So this method is clearly not correct.

Any help on the correct method would be appreciated

iNoob
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  • What would have lasted 7 days will now last 10. – it's a hire car baby Mar 30 '17 at 20:01
  • Im not sure how that is helpful, would you care to elaborate? – iNoob Mar 30 '17 at 20:03
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    Hint: suppose each boy eats $x$ per day. Then how much do $10$ boys eat in $14$ days? That tells you how much food you have (in $x$ units) and that should be enough to solve the problem – lulu Mar 30 '17 at 20:04
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    There were 10 people, now there are 7. So the time food lasts will change in the inverse proportion. – it's a hire car baby Mar 30 '17 at 20:05
  • It depends on the kind of food. If the food expire at the 14 days then it will be the same independently of the ill childs. – Masacroso Mar 30 '17 at 20:05
  • Ok think ive got this, so the original ration would have been 10:14 this has decreased to 7:10 so 14 / 7 = 2 x 10 = 20 ? – iNoob Mar 30 '17 at 20:09
  • It was x:10=14. Now it's x:7=? So x=140. Find the ? – it's a hire car baby Mar 30 '17 at 20:23
  • It really helps to use dimensional analysis on this one. Dimensional analysis attaches the units (such as boys, days, etc.) to each quantity when performing calculations. For example 10 boys * 14 days = 140 boy-days worth of food. Then how many days does 140 boy-days of food last with 7 boys? The only way to get days from this is divide boys-days by boys. So 140 boy-days / 7 boys = 20 days. – Χpẘ Mar 31 '17 at 16:15

4 Answers4

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First, notice that $\frac{10}{14}$ is not food per child, but rather child per day.

The important ratio here is not food per child, or day per child or anything like that. Its the amount of children before and after the illness. It is also important to note that number of children and days are inversely proportional. Meaning that if the number of boys goes up, number of days go down. So: $$\frac{days\ after\ illness}{days\ before\ illness}=\frac{boys\ before\ illness}{boys\ after \ illness}$$ $$\frac{days\ after\ illness}{14}=\frac{10}{7}$$ by $14$.

Simply put, you want to scale the ratio $\frac{10}{7}$ $$days\ after\ illness=14\cdot\frac{10}{7}=20$$

Dmitry Myronenko
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At the rate 10 people eat it would've lasted 14 days. But now there are only 7 to feed:

$\dfrac{10}{7}\times14=20$

Jaideep Khare
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it's a hire car baby
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10 boys * 3 meal/boy-day * 14 day = 420 meals

7 boys * 3 meal/boy-day * x day = 420 meals

21x =420

x = 20 days

Cheers

Pacco
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"UNIT_OF_FOOD"...that supports one boy for one day

"ALL"... all the food that we have available

"X"... number of days we'll last now

so...

14 * 10 * UNIT_OF_FOOD = ALL

X * 7 * UNIT_OF_FOOD = ALL

14 * 10 * UNIT_OF_FOOD = X * 7 * UNIT_OF_FOOD

14 * 10 = X * 7

X = 20

Blix
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