## Basic College Mathematics (10th Edition)

Published by Pearson

# Chapters 1-9 - Cumulative Review Exercises - Page 704: 35

#### Answer

Brian needs $8\frac{1}{3}$ cups of tomato sauce to make $2\frac{1}{2}$ times the usual amount of spaghetti sauce.

#### Work Step by Step

Let $x$ = the number of cups of tomato sauce Brian needs Brian use $3\frac{1}{3}$ cups of tomato sauce for 1 spaghetti sauce recipe. Brian needs to use $x$ cups of tomato sauce for $2\frac{1}{2}$ times the usual amount of his spaghetti sauce recipe. Ratio and proportion can be used to solve this problem. Setting up the ratio and proportion gives $$\dfrac{3\frac{1}{3}}{1} = \dfrac{x}{2\frac{1}{2}}$$ Converting the mixed numbers to improper fractions give: $$\dfrac{\frac{10}{3}}{1}=\dfrac{x}{\frac{5}{2}}$$ Cross-multiply to obtain: $$1(x) = \frac{10}{3} \cdot \frac{5}{2} x=\frac{50}{6} \\x=8\frac{2}{6} \\x=8\frac{1}{3}$$ Thus, Brian needs $8\frac{1}{3}$ cups of tomato sauce to make $2\frac{1}{2}$ times the usual amount of spaghetti sauce.

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