Problem Solving

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:44 pm

On the day of the performance of a certain play, each ticket that regularly sells for less than $10.00 is sold for half price plus $0.50, and each ticket that regularly sells for $10.00 or more is sold for half price plus $1.00. On the day of the performance, a person purchases a total of y tickets, of which x regularly sell for $9.00 each and the rest regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets ?

(A) 7y - 2x
(B) 12x - 7y
(C) (9x +12y)/3
(D) 7y + 4x
(E) 7y + 5x

Answer: A
Source: Official guide

GIVEN: A TOTAL of y tickets are sold

GIVEN: x tickets regularly sell for $9.00 each. The SALE price = $9/2 + $0.50 = $5
So, these x tickets will cost a total of 5x dollars

GIVEN: The remaining tickets regularly sell for $12.00 each. The SALE price = $12/2 + $1.00 = $7
If there are y tickets in TOTAL, and x tickets have a sale price of $5 per ticket, the remaining y-x tickets have a sale price of $7 per ticket
So, these y-x tickets will cost a total of 7(y-x) dollars

So the TOTAL amount paid for all white tickets = 5x + 7(y-x)
= 5x + (7y - 7x)
= 7y - 2x

Answer: A

Cheers,
Brent