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Jeans Discount

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by student22 » Mon Apr 19, 2010 1:15 pm
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 two discounts rates is 22 percent, what is the discount rate on Pony jeans?

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%

OA: B

I'm having alot of trouble with this one for some reason.

I'm going to post my work, so hopefully somebody can point out an easier way. No backsolving please, only algebra or logic. I'm slow with arithmetic, so backsolving would easily eat 5 minutes of the question for me.

18(2) + 15(3) = 81
F + P = 22

81 - 3(15(1 - F) + 2(18(1 - P) = 9
-45 - 45F + 36 - 36P = -72
-45F - 36P = 9
-5F - 4p = 1
-5(P - 22) - 4P = 1
-9P = -109
P =~ 12

22- 12 = 10. B.
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by kevincanspain » Mon Apr 19, 2010 2:49 pm
student22 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 two discounts rates is 22 percent, what is the discount rate on Pony jeans?

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%
Discount (%) Pony: p
Discount (%) Fox = 22 - p

Total Discount : 3(15)(22-p)/100 + 2(18)p/100 = 9

3(15)(22-p) + 2(18)p = 9(100)
5(22-p) +4p = 100

110 - p = 100
p=10
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by student22 » Mon Apr 19, 2010 3:00 pm
I see what you did, you divided each term by 100 to get the percent and set it to 9 to get the total discount.

This is much clearer (and less error prone) than the way I did it. Thanks man!
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by hooliganpete » Mon Apr 19, 2010 3:04 pm
I tried a couple of ways and came up with what I think the fastest algebraic route would be:

$9=3($15F)+2($18P) where F and P represent the relative discount rates of each jean type.

9=45F+36P simplifies to,

1=5F+4P

We are told that F+P=.22 or, F=.22-P, thus plugging this into the equation above we get,

1=5(.22-P)+4P and then we solve,

1=1.1-5P+4P --> 1=1.1-P --> -.10=-P --> multiply both sides by -1 --> P=.10

Answer is [spoiler]B or Pony jean discount rate is 10%[/spoiler]
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by student22 » Mon Apr 19, 2010 4:16 pm
Yep, that also works. It's very similar to the previous poster's, except you used decimals for the rates, whereas he used fractions. But, either way, very simple and straight to the point.

Timed, I took almost 3 minutes using my original method, which was why I decided to ask for help. Using yours or the previous poster's I can realistically solve this in under 2 minutes.
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