Hi,

I do not know the formula to solve this word problem:

The recipe called for oatmeal and raisins in the ratio of 8 to 7.

If 3 cups of oatmeal were called for, how many cups of raisins were needed?

Thanks to anyone who can help me.

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- May 22nd 2007, 03:33 PMtired6thgraderratio formula
Hi,

I do not know the formula to solve this word problem:

The recipe called for oatmeal and raisins in the ratio of 8 to 7.

If 3 cups of oatmeal were called for, how many cups of raisins were needed?

Thanks to anyone who can help me. - May 22nd 2007, 03:53 PMJhevon
Ratios deal with proportions. By saying the ratio of oatmeal to raisins is 8 to 7 (or 8:7 or 8/7) it means for every 8 parts oatmeal, we need 7 parts raisins. so a "whole" is made up of 8 + 7 = 15 parts in all.

if we wrote the amount of oatmeal as a fraction of the whole, it would be 8/15. similarly, if we wrote the amount of raisins as a fraction of the whole, we would write 7/15.

now let the number of cups of raisins needed be r. we must have that:

$\displaystyle 3:r = 8:7$

$\displaystyle \Rightarrow \frac {3}{r} = \frac {8}{7} $

$\displaystyle \Rightarrow \frac {r}{3} = \frac {7}{8}$

$\displaystyle \Rightarrow r = 3 \cdot \frac {7}{8}$

$\displaystyle \Rightarrow r = \frac {21}{8}$ cups

an alternative meathod would be to let the whole be x, since the fraction of the whole that is oatmeal is 8/15 we must have:

$\displaystyle \frac {8}{15} \cdot x = 3$

$\displaystyle \Rightarrow x = \frac {45}{8}$

Let $\displaystyle r$ be the cups of raisins needed. Since the fraction of the whole that is raisins is 7/15, we must have

$\displaystyle \frac {7}{15} \cdot \frac {45}{8} = r$

$\displaystyle \Rightarrow r = \frac {21}{8}$ cups