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?
A: 7 banana splits, 5 sundaes
B: 6 banana splits, 8 sundaes
C: 5 banana splits, 7 sundaes
D: 11 banana splits, 9 sundaes
Let's denote the number of sundaes as S and the number of banana splits as B.
From the given information, we can form two equations:
1) S = B + 2 (The number of sundaes is 2 more than the number of banana splits)
2) 3S + 2B = 31 (The total revenue from selling sundaes and banana splits is $31)
Substituting the value of S from equation 1 into equation 2, we get:
3(B + 2) + 2B = 31
3B + 6 + 2B = 31
5B + 6 = 31
5B = 25
B = 5
Substituting the value of B back into equation 1, we get:
S = 5 + 2
S = 7
Therefore, the Ice Cream Shop sold 7 sundaes and 5 banana splits.
The correct answer is C: 5 banana splits, 7 sundaes.