The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $87,100 for sales and $49,600 for service. Find the total costs of each department.
A)sales = 69,500, service = 59,000
B)sales = 99,000, service = 59,500
C)sales = 87,100, service = 49,600
D)sales = 98,000, service = 59,000
E)sales = 99,000, service = 59,000

Question

The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $87,100 for sales and $49,600 for service. Find the total costs of each department. ​
A)sales = 69,500, service = 59,000
B)sales = 99,000, service = 59,500
C)sales = 87,100, service = 49,600
D)sales = 98,000, service = 59,000
E)sales = 99,000, service = 59,000

Quizplus · Accepted Answer

Let x be the total costs of the sales department and y be the total costs of the service department.
From the given information, we have:
- The sales department charges 10% of its total monthly costs to the service department, so 0.1x is added to y.
- The service department charges 20% of its total monthly costs to the sales department, so 0.2y is added to x.
We can set up the following system of equations:
y = 0.1x + 49,600   (equation 1)
x = 0.2y + 87,100   (equation 2)
We can solve this system using substitution, elimination, or another method. One way is to substitute equation 1 into equation 2, to eliminate y:
x = 0.2(0.1x + 49,600) + 87,100
x = 0.02x + 9,920 + 87,100
0.98x = 97,020
x = 99,000
Then we can substitute x = 99,000 into equation 1, to find y:
y = 0.1(99,000) + 49,600
y = 59,500
Therefore, the total costs of the sales department is $99,000 and the total costs of the service department is $59,500. The answer is B.

The Sales Department of an Auto Dealership Charges 10% of Its