Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 5 - Ratio and Proportion - 5.5 Solving Application Problems with Proportions - 5.5 Exercises - Page 366: 42

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
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