Three sisters run a landscaping business. they charge $260 for each job. if the oldest sister earns 50 percent more than the middle sister and if the youngest sister earns 50 percent less than the oldest sister how much does each sister earn

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