## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Exercise Set - Page 831: 36

#### Answer

The prices (in dollars) are: one gallon of milk $3.5$, one bottle of water $1.5$, and one snack-size bag of chips $0.75$

#### Work Step by Step

Step 1. Assume the prices (in dollars) are: one gallon of milk $x$, one bottle of water $y$, and one snack-size bag of chips $z$ Step 2. Based on the given conditions, we have $\begin{cases} x+7y+4z=17\\y=2z\\x=y+2 \end{cases}$ Step 3. Adding the last two equations, we have $x=2z+2$ Step 4. Using the substitution of $x,y$ in the first equation, we have $2z+2+7(2z)+4z=17$, which gives $20z=15$ and $z=0.75$ Step 5. Back substitute the known values to get: $x=3.5$ and $y=1.5$ Step 6. We conclude the prices (in dollars) are: one gallon of milk $3.5$, one bottle of water $1.5$, and one snack-size bag of chips $0.75$

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