Question

shelley and michelle need to make a total of $6,080 to reach their quota. shelley sold eight less than four times as many gifts as michelle did. if each gift sells for $40, how many more gifts did shelley sell than michelle?

Explanation:

Step1: Define variables

Let \( x \) be the number of gifts Michelle sold. Then Shelley sold \( 4x - 8 \) gifts.

Step2: Calculate total revenue

The total revenue from both is \( 40(x + 4x - 8) = 6080 \).

Step3: Simplify the equation

First, simplify inside the parentheses: \( x + 4x - 8 = 5x - 8 \). Then the equation becomes \( 40(5x - 8) = 6080 \).

Step4: Solve for \( x \)

Divide both sides by 40: \( 5x - 8 = \frac{6080}{40} = 152 \). Then add 8 to both sides: \( 5x = 152 + 8 = 160 \). Divide by 5: \( x = \frac{160}{5} = 32 \).

Step5: Find Shelley's sales

Shelley sold \( 4x - 8 = 4(32) - 8 = 128 - 8 = 120 \) gifts.

Step6: Find the difference

Subtract Michelle's sales from Shelley's: \( 120 - 32 = 88 \).

Answer:

88