A contractor rented a sander for 5h and a polisher for $50. For another job, she rented the sander for 4h and the polisher for 8h. The rental fees for the job totalled $56. Find the hourly rate charged for each tool.

Answer 1

Sander = X Dollars / hr.
Polisher = Y Dollars/hr

Eq1: 5X + 5Y = 60.
Eq2: 4X + 8Y = 56.

Multiply Eq1 by -4 and Eq2 by 5 and add.
-20X - 20Y = -200.
20X + 40Y = 280.

20Y = 80,
Y = 80 / 20 = 4.

Substitute 4 for Y in Eq1:
5X + 5*4 = 50,
5X + 20 = 50,
5X = 50 - 20 = 30,
X = 30 / 5 = 6.