homework help!?

Question

Jaden received these two estimates from a moving company. Write and solve a system of equations to determine the hourly loading/unloading fee and the mileage charge for the truck rental.

Situation A: He hires 5 helpers to load and unload the truck and travels 80 miles on back roads for a total cost of $780.

Situation B: He hires 6 helpers to load and unload the truck and takes a highway route which adds 20 miles to the trip but gets the truck to the destination faster for a total cost of $960.

Answer 1

in situation a we have:

780 = 5x + 80y (1)

in situation b:

960 = 6x + 100y (2)

where,

x is load/unload fee (one fee per trip, per worker) and ,

y is the mileage charge (dollar/mile)

We need to find x,y such that (1),(2) are both satisfied simultaneously

To do that we solve for either x or y in terms of the remaining variable using equations (1) or (2),

We then substitute that value into the remaining equation, and if the system has a solution we will find it here.

I will start by isolating x in (1), which gives

5x = 780 - 80y

x = 156 - 16y (3)

next we substitute (3) into (2) and solve for y

960 = 6(156 - 16y) + 100y

= 936 - 96y + 100y

= 936 + 4y

or,

4y = 24

y = 6

substituting back into (3) gives

x = 156 - 16*6

= 60

Please do verify that I made no errors in calculation, but this is how you solve a linear system of 2 equations. In your example we find the solution:

x = 60

y = 6

Please let me know if you need clarification on anything!

Best,

Carmine