Zane received a quote to move his belongings to his new house. The estimate from the mover is $675 for 6 hours of packing and 5 hours of moving. Zane thinks he can reduce his cost by doing some of the packing and moving himself. If he does, the cost will decrease to $425 for 4 hours of packing and 3 hours of moving. If the mover charges a set hourly rate for packing and another set hourly rate for moving, what are these hourly rates?

Question

Mathematics

Samantha Lyons

23 May, 12:15

Zane received a quote to move his belongings to his new house. The estimate from the mover is $675 for 6 hours of packing and 5 hours of moving. Zane thinks he can reduce his cost by doing some of the packing and moving himself. If he does, the cost will decrease to $425 for 4 hours of packing and 3 hours of moving. If the mover charges a set hourly rate for packing and another set hourly rate for moving, what are these hourly rates?

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Answers (1)

Know the Answer?

Tanya Hahn · Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that:

-The estimate from the moving is $675 for 6 hours of packing and 5 hours of moving.

- The cost will decrease to $425 for 4 hours of packing and 3 hours of moving.

x: rate for packing.

y: rate for moving.

6x+5y=675

4x+3y=425

2. When you solve the system of equations shown above, you obtain:

x=50

y=75

Therefore, the answer is: $50 (Rate for packing) and $75 (Rate for moving).