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Salim wants to purchase tickets from a v...

Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation T = 15n + 12 represents the total amount T, in dollars, Salim will pay for n tickets. What does 12 represent in the equation?

A

The price of one ticket, in dollars

B

The amount of the service fee, in dollars

C

The total amount, in dollars, Salim will pay for one ticket

D

The total amount, in dollars, Salim will pay for any number of tickets

Text Solution

Verified by Experts

The correct Answer is:
B
The total amount T, in dollars, Salim will pay for n tickets is given by T = 15n + 12, which consists of both a per-ticket charge and a one-time service fee. Since n represents the number of tickets that Salim purchases, it follows that 15n represents the price, in dollars, of n tickets. Therefore, 15 must represent the per-ticket charge. At the same time, no matter how many tickets Salim purchases, he will be charged the $12 fee only once. Therefore, 12 must represent the amount of the service fee, in dollars.
Choice A is incorrect. Since n represents the total number of tickets that Salim purchases, it follows that 15n represents the price, in dollars, of n tickets, excluding the service fee. Therefore, 15, not 12, must represent the price of 1 ticket. Choice C is incorrect. If Salim purchases only 1 ticket, the total amount, in dollars, Salim will pay can be found by substituting n = 1 into the equation for T. If n = 1, T = 15(1) + 12 = 27. Therefore, the total amount Salim will pay for one ticket is $27, not $12. Choice D is incorrect. The total amount, in dollars, Salim will pay for n tickets is given by 15n + 12. The value 12 represents only a portion of this total amount. Therefore, the value 12 does not represent the total amount, in dollars, for any number of tickets.
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