Answer:
The number of hours Jackie worked = 80hours
Step-by-step explanation:
Last summer:
Jackie made $960
Rachel made $960
let number of hours Jackie worked = x
Rachel worked 16 hours more than Jackie:
Number of hours Rachel worked = x + 16
if Jackie earned $y per hour
Rachel earned $2 less per hour = y-2
Jackie: 960 = x × y = xy
Rachel: 960 = (x+16)(y-2)
960 = xy -2x +16y -32
recall xy = 960, insert the value for xy
960 = 960 - 2x +16y -32
- 2x +16y -32 = 0
2x -16y = -32
x-8y = -16
x = 8y-16
recall xy = 960, insert the expression for x
(8y-16)y = 960
8y² -16y = 960
y² -2y - 120 = 0
y²+10y-12y -120 = 0
y(y+10) -12(y+10) = 0
(y-12) = 0 or (y+10) = 0
y = 12 or -10
since y can't be negative, y = 12
x = 8y-16
x = 8(12) -16 = 80
The number of hours Jackie worked = x = 80 hours
