## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Review Exercises - Page 877: 8

#### Answer

Three apples and two avocados must be taken to get 1000 calories and 100 grams of carbohydrates.

#### Work Step by Step

Let us assume the number of apples be x and the number of avocados be y that need to be taken to have 1000 calories and 100 grams of carbohydrates. So, the equation becomes: $100x+350y=1000$ Also, we know that the carbohydrates contained by one apple and one avocado are $24$ and $14$: $24x+14y=100$ Then, multiply, the equation $24x+14y=100$ by 25, $600x+350y=2500$ And subtract $100x+350y=1000$ from $600x+350y=2500,$ \begin{align} & 500x=1500 \\ & x=3 \end{align} Put x = 3 in $24x+14y=100$, \begin{align} & 24\times 3+14y=100 \\ & 14y=100-72 \\ & 14y=28 \\ & y=2 \end{align} So, $x=3,y=2$. Hence, three apples and two avocados must be taken to get 1000 calories and 100 grams of carbohydrates.

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