Peter and Jill each worked a different number of days, but earned the same amount of money. Use these clues to determine how many days each worked. Peter earned \( \$ 30 \) a day. Jill earned \( \$ 40 \) a day. Peter worked two more days than Jill. Jill worked \( \square \) days.

Let's break it down! Since Peter earned \( \$30 \) per day and worked two more days than Jill, we can represent the number of days Jill worked as \( x \). Therefore, Peter worked \( x + 2 \) days. Now, we can set up the equations based on their earnings: - Peter’s total earnings: \( 30(x + 2) \) - Jill’s total earnings: \( 40x \) Since they earned the same amount of money, we can equate the two: \[ 30(x + 2) = 40x \] Expanding this gives us: \[ 30x + 60 = 40x \] Now, isolate \( x \): \[ 60 = 40x - 30x \] \[ 60 = 10x \] \[ x = 6 \] So, Jill worked \( 6 \) days, and Peter, who worked two more days, worked \( 8 \) days. Hence, the answer is Jill worked \( 6 \) days and Peter worked \( 8 \) days.