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?

Question

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.