y = − 0.005 x 4 + 0.05 x 3 − 0.086 x 2 − 0.04 x + 2.52 y = - 0.005 x 4 + 0.05 x 3 - 0.086 x 2 - 0.04 x + 2.52

First: $65

Second: $115

Step-by-step explanation:

We write equations for each part of this situation.

The Total Charge

Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.

The Sum of the Rates

Since the first's rate is a and the second is b, we can write a+b=180 since their sum is 180.

We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.

For a+b=180, rearrange to b=180-a and substitute into 15a+5b=1550.

15a + 5 (180-a)=1550

15a+900-5a=1550

10a+900-900=1550-900

10a=650

a=$65 was charged by the first mechanic.

We substitute to find the second mechanic's rate.

65+b=180

65-65+b=180-65

b= $115 was charged by the second mechanic