At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a

by Vincen » Sat Jan 30, 2021 9:42 pm

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At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12

Answer: A

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sat Jan 30, 2021 9:42 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running

by Scott@TargetTestPrep » Tue Feb 09, 2021 5:31 pm

Vincen wrote: ↑
Sat Jan 30, 2021 9:42 pm
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12

Answer: A

Solution:

We can let x be the price of each pizza after the $2 discount. Therefore, the price of each pizza before the discount is x + 2 dollars and we can create the equation:

[96 / (x + 2)] + 4 = 96/x

Multiplying the equation by x(x + 2), we have:

96x + 4x(x + 2) = 96(x + 2)

96x + 4x^2 + 8x = 96x + 192

4x^2 + 8x - 192 = 0

x^2 + 2x - 48 = 0

(x - 6)(x + 8) = 0

x = 6 or x = -8

Since x can’t be negative, x = 6.

Answer: A

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