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

Answer:The youngest sister earns $60The middle sister earns $80The oldest sister earns $120Step-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 - - - - - - - - -1the oldest sister earns 50 percent more than the middle sister. This means z = y + 50 percent of yz = y + 0.5y = 1.5yThe youngest sister earns 50 percent less than the oldest sister. This meansx = z - 50 percent of zx = z - 0.5z = 0.5z x = 0.5z Substituting z = 1.5y in x = 0.5z, we have x = 0.5 × 1.5 = 0.75ySubstituting x = 0.75y and z = 1.5y into equation 1, it becomes0.75y + y + 1.5y = 2603.25y = 260y = 260/3.25 = $80z = 1.5y = 1.5 × 80 = $120x = 0.5z = 0.5 × 120 = $60