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 $\text{15 mg}$.
