Question

The Ice Cream Shop sells sundaes for $3 and banana splits for $2. On a hot summer day, the shop sold 2 more sundaes than banana splits and made $31.



How many sundaes and banana splits did the Ice Cream Shop sell?
Responses

A 7 banana splits, 5 sundaes7 banana splits, 5 sundaes

B 6 banana splits, 8 sundaes6 banana splits, 8 sundaes

C 5 banana splits, 7 sundaes 5 banana splits, 7 sundaes

D 11 banana splits, 9 sundaes

Answer 1

Let \( x \) represent the number of banana splits sold, and \( y \) represent the number of sundaes sold. According to the problem, we have the following equations:

1. \( y = x + 2 \) (the shop sold 2 more sundaes than banana splits)
2. \( 3y + 2x = 31 \) (the total revenue from sundaes and banana splits)

Now, we can substitute the first equation into the second equation.

Substituting \( y \) in the second equation:

\[
3(x + 2) + 2x = 31
\]
\[
3x + 6 + 2x = 31
\]
\[
5x + 6 = 31
\]
\[
5x = 31 - 6
\]
\[
5x = 25
\]
\[
x = 5
\]

Now, we can find \( y \):

\[
y = x + 2 = 5 + 2 = 7
\]

So, the Ice Cream Shop sold 5 banana splits and 7 sundaes.

The correct answer is:

**C: 5 banana splits, 7 sundaes**