Question

A car servicing station is running a special offer. The breakdown of the cost for different services is given below.

•Membership Fee: $50 (one-time cost)

•Air Freshener Cost: $4 per car per month

•Washing Cost: $10 per car per month

•Tire Replacement Cost: $400 per car

•Tire Pressure Check Cost: $15 per month

The total cost for 12 months of this service for n cars is given by the expression below.

568n + 230

Which statement best describes the constant in the expression?

A. It is the total cost of the air freshener, washing, and tire replacement for 12 months.

B. It is the monthly cost of the membership fee and tire pressure check.

C. It is the total cost of the meme worship fee and the tire pressure check for 12 months.

D. It is the monthly cost of the air freshener, washing, and tire replacement.

Answer 1

Answer: The total cost of the meme worship fee and the tire pressure check for 12 months.

Explanation:

Let n be the number of cars .

Given: The breakdown of the cost for different services is given below.

Membership Fee: $50 (one-time cost) → constant

Air Freshener Cost: $4 per car per month

⇒ Air Freshener Cost for 12 months per car =
`4*12* n=48n`

Washing Cost: $10 per car per month

⇒ Washing Cost for 12 months=
`10*12* n=120n`

Tire Replacement Cost: $400 per car

⇒ Tire Replacement Cost for n car=
`400n`

Tire Pressure Check Cost: $15 per month

⇒ Tire Pressure Check Cost for 12 months=
`15*12=\$180` → constant

Now, the total cost for 12 months of this service for n cars is given by the expression.

`50+48n+120n+400n+180\\=48n+400n+120n+50+180\\=568n+230`

Here the sum of constants =
`180+50=230` represents the the total cost of the meme worship fee and the tire pressure check for 12 months.

Answer 2

C. It is the total cost of the membership fee and the tire pressure check for 12 months.

Explanation:

The constant represents the sum of costs that are not "per car." Those are only "membership fee" ($50) and "tire pressure check" ($15/mo × 12 mo = $180).