The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.
The correct answer and explanation is:
Let the number of banana splits sold be represented by xx. Since the shop sold 8 more sundaes than banana splits, the number of sundaes sold is x+8x + 8.
The price of a sundae is $2 and the price of a banana split is $3. The total revenue from sundaes is therefore 2(x+8)2(x + 8), and the total revenue from banana splits is 3x3x.
The total revenue for the day is $156. Therefore, the equation for the total revenue is: 2(x+8)+3x=1562(x + 8) + 3x = 156
Now, expand and simplify the equation: 2x+16+3x=1562x + 16 + 3x = 156 5x+16=1565x + 16 = 156
Next, subtract 16 from both sides of the equation: 5x=1405x = 140
Now, divide both sides by 5 to solve for xx: x=28x = 28
So, 28 banana splits were sold. To find the number of sundaes sold, we substitute x=28x = 28 into x+8x + 8: 28+8=3628 + 8 = 36
Therefore, the shop sold 36 sundaes.
To check, calculate the total revenue:
- Revenue from sundaes: 36×2=7236 \times 2 = 72
- Revenue from banana splits: 28×3=8428 \times 3 = 84
Total revenue: 72+84=15672 + 84 = 156, which matches the given amount.
Thus, the shop sold 28 banana splits and 36 sundaes.