ratio formula

**tired6thgrader** · May 22nd 2007, 03:33 PM

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.

**Jhevon** · May 22nd 2007, 03:53 PM

Originally Posted by tired6thgrader

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.

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:

$3:r = 8:7$

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

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

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

$\Rightarrow r = \frac {21}{8}$ 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:

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

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

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

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

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

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