# Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for$2.50 per pound. If she made $337.50, how many pounds of peaches did she sell? Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for$1.75 per pound and peaches for $2.50 per pound. If she made$337.50, how many pounds of peaches did she sell?

See a solution process below:

#### Explanation:

First, lets call:

$a$ the number of pounds of apples Mo sold.

$p$ the number of pounds of peaches Mo sold.

Then we can write these two equations from the information in the problem:

Equation 1: $a + p = 165$

Equation 2: $1.75 a + 2.50 p = 337.50$

Step 1) Solve the first equation for $a$:

$a + p = 165$

$a + p - \textcolor{red}{p} = 165 - \textcolor{red}{p}$

$a + 0 = 165 - p$

$a = 165 - p$

Step 2) Substitute $\left(165 - p\right)$ for $a$ in the second equation and solve for $p$:

$1.75 a + 2.50 p = 337.50$ becomes:

$1.75 \left(165 - p\right) + 2.50 p = 337.50$

$\left(1.75 \times 165\right) - \left(1.75 \times p\right) + 2.50 p = 337.50$

$288.75 - 1.75 p + 2.50 p = 337.50$

$288.75 + \left(- 1.75 + 2.50\right) p = 337.50$

$288.75 + 0.75 p = 337.50$

$- \textcolor{red}{288.75} + 288.75 + 0.75 p = - \textcolor{red}{288.75} + 337.50$

$0 + 0.75 p = 48.75$

$0.75 p = 48.75$

$\frac{0.75 p}{\textcolor{red}{0.75}} = \frac{48.75}{\textcolor{red}{0.75}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.75}}} p}{\cancel{\textcolor{red}{0.75}}} = 65$

$p = 65$

Because the problem only asks for the number of pounds of peaches we do not need to go any further.

Mo sold $\textcolor{red}{65}$ pounds of peaches.

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