Question

10) You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.

a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.

Answer 1

a) 10

b) Number of hours of phone support (per month).

c) Total bill (per month).

d) y = 35x + 10

e) 2.5 hours

Explanation:

The company bills you at a rate of:

• $10 per month
• $35 per hour

Part a

The fixed cost (the constant) is the cost per month ⇒ $10.

Part b

The independent variable is the variable that is not affected by any other variables.

Therefore, the independent value (variable x) is the number of hours of phone support per month.

Part c

A dependent variable is the variable that is affected by the other variable.

Therefore, the dependent value (variable y) is the total bill (in dollars) per month.

Part d

The equation that describes the given situation is:

• 
  `y = 35x + 10`

Part e

To calculate how many hours of phone support was needed for a bill of $97.50, substitute y = 97.5 into the equation from part d and solve for x.

`\implies 35x+10=97.5`

`\implies 35x+10-10=97.5-10`

`\implies 35x=87.5`

`\implies (35x)/(35)=(87.5)/(35)`

`\implies x=2.5`

Therefore, 2.5 hours of phone support was needed last month.