Question

A bakery sells 3 muffins for every 5 pizza pies. The bakery sold a total of 24 muffins and pizza pies together. How many of each kind did the bakery sell?
6 muffins and 18 pizza pies
9 muffins and 15 pizza pies
15 muffins and 6 pizza pies
18 muffins and 6 pizza pies

Answer 1

Let the number of muffins sold be \( m \) and the number of pizza pies sold be \( p \).

From the problem statement, we have two key pieces of information:
1. The bakery sells 3 muffins for every 5 pizza pies, which can be written as the ratio:
\[
\frac{m}{p} = \frac{3}{5}
\]
This can be rearranged to:
\[
5m = 3p \quad (1)
\]

2. The total number of muffins and pizza pies sold is 24:
\[
m + p = 24 \quad (2)
\]

We can solve these two equations. From equation (2), we can solve for \( p \):
\[
p = 24 - m
\]

Now substitute this expression for \( p \) into equation (1):
\[
5m = 3(24 - m)
\]
Expanding the right-hand side:
\[
5m = 72 - 3m
\]
Now, add \( 3m \) to both sides:
\[
5m + 3m = 72
\]
\[
8m = 72
\]
Now divide both sides by 8:
\[
m = 9
\]

Now, substitute \( m = 9 \) back into equation (2) to find \( p \):
\[
9 + p = 24
\]
\[
p = 24 - 9 = 15
\]

So, the bakery sold 9 muffins and 15 pizza pies. Therefore, the correct answer is:
**9 muffins and 15 pizza pies.**