Value mixture problem

Question

Two mechanics work on the car. The first mechanic charge $105 per hour, and the second mechanic charge $115 per hour. The mechanics work for a combined total of 35 hours, and together they charge a total of $3825. How long did each mechanic work?

Answer 1

We have 2 unknowns, therefore, we need 2 equations to solve this.

Let x= mechanic 1's hrs worked

y= mechanic 2's hrs worked

Eq. I: x+y=35--->y=35-x

Eq. II: 105x+115y=3825

Substituting the value for y from Eq. I into Eq. II we can solve for x:

105x+115y=3825 Eq. II

105x+115(35-x)=3825 substitute for y

105x+4025-115x=3825 simplify

105x-115x=3825-4025 combine like-terms

-10x=-200 simplify

x=-200/-10 divide both sides by -10

x=20 solve for x

Using this value for x in Eq. I we can now solve for y:

x+y=35 Eq. I

20+y=35 substitute for x

y=35-20 subtract 20 from both sides to isolate y

y=15 solve for y

Putting these values into both our equations we see that the answers are correct. Therefore, mechanic 1 worked 20 hrs and mechanic 2 worked 15 hrs.