Question

1. a local girls club sold 176 boxes of cookies and made a total of $520. they sold two types of cookies: chocolate mint for $3.50 a box and peanut butter patties for $2.75 a box. how many chocolate mint boxes did they sell?

Explanation:

Step1: Define variables

Let \( x \) be the number of chocolate mint boxes sold and \( y \) be the number of peanut butter patties boxes sold.
We know two equations:

1. \( x + y = 176 \) (total number of boxes)
2. \( 3.50x + 2.75y = 520 \) (total money made)

From the first equation, we can express \( y \) as \( y = 176 - x \).

Step2: Substitute \( y \) into the second equation

Substitute \( y = 176 - x \) into \( 3.50x + 2.75y = 520 \):
\[

$$\begin{align*} 3.50x + 2.75(176 - x) &= 520\\ 3.50x + 2.75\times176 - 2.75x &= 520\\ 3.50x - 2.75x + 484 &= 520\\ 0.75x + 484 &= 520 \end{align*}$$

\]

Step3: Solve for \( x \)

Subtract 484 from both sides:
\[
0.75x = 520 - 484\\
0.75x = 36
\]
Divide both sides by 0.75:
\[
x = \frac{36}{0.75}\\
x = 48
\]

Answer:

48