## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Test - Page 879: 13

#### Answer

The cholesterol content in an ounce of shrimp is $42\text{ mg}$ and the cholesterol content in an ounce of scallops is $\text{15 mg}$.

#### Work Step by Step

Consider the amount of cholesterol in one ounce of shrimp to be $x$ and the amount of cholesterol in one ounce of scallops to be $y$. Write the equation which represents the cholesterol from $3$ ounces of shrimp $x$ and $2$ ounces of scallops $y$ for a total of $156\text{ mg}$. $3x+2y=156$ …… (1) The $5$ ounces of shrimp and $3$ ounces of scallops include $45\text{ mg}$ of cholesterol less than the suggested maximum daily intake which is $300\text{ mg}$. The amount of cholesterol from $5$ ounces of shrimp and $3$ ounces of scallops is, $300\text{ mg}-45\text{ mg}=255\text{ mg}$ Write the equation which represents the cholesterol from $5$ ounces of shrimp $x$ and $3$ ounces of scallops $y$ as $\text{255 mg}$. $5x+3y=255$ …… (2) Multiply both sides of equation (1) by $-3$. \begin{align} & -3\left( 3x+2y \right)=-3\left( 156 \right) \\ & -9x-6y=-468 \end{align} …… (3) Multiply both sides of equation (2) by $2$ \begin{align} & 2\left( 5x+3y \right)=2\left( 255 \right) \\ & 10x+6y=510 \end{align} …… (4) Add equation (3) and equation (4). \begin{align} & \underline{\begin{align} & -9x-6y=-468 \\ & 10x+6y=510 \end{align}} \\ & \text{ }x\text{ }=42 \\ \end{align} Substitute $x=42$ in the equation (1). \begin{align} & 3\left( 42 \right)+2y=156 \\ & 126+2y=156 \\ & 2y=30 \\ & y=15 \end{align} Therefore, the cholesterol content in an ounce of shrimp is $42\text{ mg}$ and the cholesterol content in an ounce of scallops is $\text{15 mg}$.

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