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A bookstore has a shelf that contains biographies which

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by Gmat_mission » Sun Mar 11, 2018 8:46 am
A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25

[spoiler]OA=E[/spoiler].

I got confused trying to set the equations to solve this PS question. Can any expert show me what is the best way to solve this question. Please. Thanks in advanced.
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by Jay@ManhattanReview » Mon Mar 12, 2018 5:26 am
Gmat_mission wrote:A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25

[spoiler]OA=E[/spoiler].

I got confused trying to set the equations to solve this PS question. Can any expert show me what is the best way to solve this question. Please. Thanks in advanced.
Say the discount rate on biographies = x%, thus, the discount rate on mysteries = (35 - x)%

Total saving = 5*(20)*x% + 3*(12)*(35 - x)% = 19

Upon solving, we get x = 10%, thus, the discount rate on mysteries = (35 - x)% = 35 - 10 = 25%.

The correct answer: E

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Tue Mar 13, 2018 4:15 pm
Gmat_mission wrote:A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25
We can let x = the percent by which the biographies are discounted, and thus, (35 - x) = the percent by which the mysteries are discounted. Just as we can express, say, 42% as 42/100, we will express x% as x/100, and, similarly, (35 - x)% is re-expressed as (35 - x)/100. We can create the following equation:

5 * 20 * x/100 + 3 * 12 * (35 - x)/100 = 19

Multiplying both sides by 100, we have:

100x + 36(35 - x) = 1900

100x + 1260 - 36x = 1900

64x = 640

x = 10

Thus, the mysteries are discounted by 35 - 10 = 25 percent.

Answer: E

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