Solving a value mixture problem using a system of linear equations
Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $80 per hour. The mechanics worked fa
combined total of 35 hours, and together they charged a total of $2300. How long did each mechanic work?
First mechanic: hours

Question

Answered

Answer :

regalmocha17 regalmocha17 · Answer 1 · 2024-05-19T10:24:58-04:00

Answer:

Mechanic 1 worked 20 hours and mechanic 2 worked 15 hours.

Step-by-step explanation:

First mechanic can be represented as x and the second mechanic can be represented as y.

We can set up two equations.

55x + 80y = 2300

x + y = 35

x = hours worked by 1st mechanic

y = hours worked by 2nd mechanic

Now we can solve for each variable.

55x + 80y = 2300

x + y = 35

Isolate the y variable.

x = 35 - y

replace x

55(35 - y) + 80y = 2300

1925 - 55y + 80y = 2300

combine like terms

1925 + 25y = 2300

solve for y

2300 - 1925 = 25y

375 = 25y

y = 15

Now that we have y, we can plug it in and solve for x.

x + y = 35

x + 15 = 35

x = 35 - 15

x = 20

Thus, mechanic one worked 20 hours while mechanic two worked 15 hours.