A bookstore has a shelf that contains biographies which

Question

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

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

MacFauz · Answer

Let B be the discount on biographies and M be the discount on mysteries

So., B + M = 0.35 -----(1)

And

(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
 
--> 100(1-(1-B)) + 36(1-(1-M) = 19

100B + 36M = 19 ------(2)

Solving 1 & 2., we get M = 0.25 = 25%

Anichka · Answer

Thanks! It works out now.

I have though a question.
In the problem it says: "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."

Doesn't that mean that when 5 biographies and 3 mysteries are purchased, the total amount will be 19 less than if the books have not been discounted, meaning, 5*20 + 3*12 = 136 (this would be if they kept the original price). But after the discount ( (5*20 - 5*20*b%) + (3*12 - 3*12*m%) = 136 - 19.
Then, the equation doesn't work.

Thank you for your reply!

MacFauz · Answer

You should note that it should be 5*20*(1-b) and 3*12*(1-m). To make it more clear.

Suppose an item costs $100. And now I am going to give a discount of 20%. The new price would not be $20 (i.e 100*0.2) rather it would be $80 (i.e 100*(1-0.2)).

When you are discounting a price P by x%, the discounted price will be  P*(1 - \frac{x}{100})  and not  \frac{P*x}{100}

Kudos Please... If my post helped.

EvaJager · Answer

Another way to translate into equations:

M - percent discount on one mystery book
B - percent discount on one biography book

B + M = 35
5x20xB/100 + 3x12xM/100 = 19 - the saving of $19 comes from the discounts, which can be directly expressed in terms of M and B, respectively, for the two types of books.

Solve the system of two equations:
B + M = 35
100B + 36M = 1900

Or:
From the answers, we can see that M should be an integer. Because 100 and 1900 are both divisible by 5, only B and E should be checked.

Answer E.

Archit143 · Answer

i didnt understand what is (1-b) and (1-m)
pls explain in detail

MacFauz · Answer

An item costs $100.

I am now going to give a discount of b% on it. So my new price would be

100 - 100*(\frac{b}{100})   =   100*(1-\frac{b}{100})

If we take b% in the decimal form. ( eg: 20% as 0.2) then the above equation would be

100*(1-b)

Kudos Please... If my post helped.

ufo9038 · Answer

I got the right answer but only after 5 mins. The difficulty is the precision in calculations. How to reduce time on these questions yet still maintain precision?! Thanks very much in advance.

ScottTargetTestPrep · Answer

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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A bookstore has a shelf that contains biographies which

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