The county government released $100,000 as an appropriation for a counseling program for at-risk teenagers.The program should run one year and the variable costs for the program are $400 per teenager per year.Within the relevant range of 50 to 150 teenagers,the fixed costs for the program are $60,000.How many teenagers can the program serve?
A) 50
B) 100
C) 150
D) 250

Question

Quizplus · Accepted Answer

The total cost of the program can be calculated by adding the fixed costs of $60,000 to the variable costs of $400 per teenager multiplied by the number of teenagers (x) served:
Total cost = $60,000 + $400x
We know that the total appropriation is $100,000, so we can set the total cost equal to this amount:
$100,000 = $60,000 + $400x
Subtracting $60,000 from both sides gives:
$40,000 = $400x
Dividing both sides by $400 gives:
x = 100
Therefore, the program can serve 100 teenagers.

The County Government Released $100,000 as an Appropriation for a Counseling