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jamesk486: Master | Next Rank: 500 Posts; Posts: 141; Joined: Wed Mar 28, 2007 9:24 pm; Thanked: 2 times; Followed by:1 members

PT question

by jamesk486 » Mon Apr 16, 2007 1:24 am

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the 2 discount rates is 22%, what is the discount rate on Pony jeans?

(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%

The answer is B...don't know how that comes out...

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Source: Beat The GMAT — Problem Solving | Mon Apr 16, 2007 1:24 am

Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Mon Apr 16, 2007 2:23 am

Let the rates of discount on Fox and Pony Jeans be x and y respectively

x + y=22 ----- 1)

Using the 2 discounts the customer saves $9

So 15*3x/100 + 18*y/100 = 9
45x + 36y = 900
5x + 4y = 100 ------ 2)

Now when you solve the 2 you will get y = 10%. Discount on Pony's jeans = 10%

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

by BTGmoderatorRO » Sun Dec 24, 2017 6:11 am

Let the discount rates on fox jeans and Pany jeans be 'm' and 'n' respectively.
Also, let the actual selling prices after discounting be 'x' and 'y' for fox and pony jeans respectively.
Without Discounts,
Three fox jean and two pony jeans cost
=3($15)+2($18)
=$81
With discounts, $9 dollar is saved.
Actual total selling price
=$(81-9)= $72
This also implies that : 3x+2y=72
The actual selling prices are the original price minus the amount of the discounts.
x= 15 - (15* $$\frac{m}{100}$$ )
15-0.15m
and y= 18-(18* $$\frac{n}{100}$$ )
18-0.18n
Putting these expressions for x and ynin
3x+2y=72
i.e 3(15-0.15m)+ 2(18-0.18n)=72
45-0.45m+36-0.36n=72
0.45m+0.36n=9....eqn 1
From the question
The discount add up to 22%
i.e m+n =22
m=22-n
substituting 22-n for m in eqn 1
0.45(22-n) + 0.36n=9
9.9-0.45n+0.36n=9
0.09n=0.9
Therefore, n=
$$\frac{0.9}{0.09}$$ =10
Since, n represents the discount rate on pony jeans thus rate = 10%.

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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

by Scott@TargetTestPrep » Mon Sep 09, 2019 9:48 am

jamesk486 wrote:Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the 2 discount rates is 22%, what is the discount rate on Pony jeans?

(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%

The answer is B...don't know how that comes out...

At the regular prices, 3 pairs of Fox jeans and 2 pairs of Pony jeans would cost 3 x 15 + 2 x 18 = 45 + 36 = $81. Since a total of $9 is saved at the discounted prices, the cost of the same 5 pairs of jeans is now $72. Since the sum of the 2 discount rates is 22%, we can let n/100 = the discount rate on Pony jeans and (22 - n)/100 = the discount rate on Fox jeans and create the equation:

3 x 15 x (1 - (22 - n)/100) + 2 x 18 x (1 - n/100) = 72

Multiplying the equation by 100, we have:

45 x (100 - (22 - n)) + 36 x (100 - n) = 7200

45 x (78 + n) + 3600 - 36n = 7200

3510 + 45n - 36n = 3600

9n = 90

n = 10

Thus, the discount rate on Pony jeans is n/100 = 10/100 = 10%.

Answer: B

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