Answer
For 18 servings:
- $5\displaystyle \frac{1}{4}$ cups water
- 9 Tbsp margarine
- $2\displaystyle \frac{1}{4}$ cups milk
- 6 cups potato flakes
Work Step by Step
We find the amount of each ingredient by setting up proportions:
Water:
$\displaystyle \frac{3\frac{1}{2}~cups}{12~servings}=\frac{n~cups}{18~servings}$
$12*n=3\frac{1}{2}*18$
$12*n=\frac{7}{2}*18$
$12*n=7*\frac{18}{2}$
$12*n=7*9$
$12*n=63$
$n=\frac{63}{12}=5\frac{1}{4}$ cups
Margarine:
$\displaystyle \frac{6~Tbsp}{12~servings}=\frac{n~Tbsp}{18~servings}$
$6*18=n*12$
$108=n*12$
$n=\frac{108}{12}=9$ Tbsp
Milk:
$\displaystyle \frac{1\frac{1}{2}~cups}{12~servings}=\frac{n~cups}
{18~servings}$
$1\frac{1}{2}*18=n*12$
$\frac{3}{2}*18=n*12$
$3*\frac{18}{2}=n*12$
$3*9=n*12$
$27=n*12$
$n=\frac{27}{12}$
$n=2\frac{1}{4}$ cups
Potato flakes:
$\displaystyle \frac{4~cups}{12~servings}=\frac{n~cups}{18~servings}$
$4*18=n*12$
$72=n*12$
$n=\frac{72}{12}$
$n=6$ cups
Alternatively, we can get the same answers by taking the results of Exercise 41 (for 6 servings) and multiplying by 3 (because $6*3=18$):
Water:
$1\displaystyle \frac{3}{4}*3=\frac{7}{4}*\frac{3}{1}=\frac{21}{4}=5\frac{1}{4}$ cups
Margarine:
$3*3=9$ Tbsp
Milk:
$\displaystyle \frac{3}{4}*3=\frac{3}{4}*\frac{3}{1}=\frac{9}{4}=2\frac{1}{4}$ cups
Potato flakes:
$2*3=6$ cups