Answer:
The youngest sister earns $60
The middle sister earns $80
The oldest sister earns $120
Step-by-step explanation:
Let x = the amount earned by the younger sister.
Let y = the amount earned by the middle sister.
Let z = the amount earned by the oldest sister.
They charge $260 for each job. This means
x + y + z = 260 - - - - - - - - -1
the oldest sister earns 50 percent more than the middle sister. This means
z = y + 50 percent of y
z = y + 0.5y = 1.5y
The youngest sister earns 50 percent less than the oldest sister. This means
x = z - 50 percent of z
x = z - 0.5z = 0.5z
x = 0.5z
Substituting z = 1.5y in x = 0.5z, we have x = 0.5 × 1.5 = 0.75y
Substituting x = 0.75y and z = 1.5y into equation 1, it becomes
0.75y + y + 1.5y = 260
3.25y = 260
y = 260/3.25 = $80
z = 1.5y = 1.5 × 80 = $120
x = 0.5z = 0.5 × 120 = $60
