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
Let's start by setting up a system of equations to represent the given information.
Let x be the number of banana splits sold.
Let x + 2 be the number of sundaes sold.
The cost of one banana split is $2, so the total revenue from banana splits is 2x.
The cost of one sundae is $3, so the total revenue from sundaes is 3(x + 2).
The total revenue from both banana splits and sundaes is $31, so we can write the equation:
2x + 3(x + 2) = 31.
Simplifying the equation:
2x + 3x + 6 = 31,
5x + 6 = 31,
5x = 25,
x = 5.
So, the Ice Cream Shop sold 5 banana splits and 5 + 2 = 7 sundaes.
Therefore the answer is:
C) 5 banana splits, 7 sundaes.