help! old GMAT Prep Q

[san2009]

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%


seemed cumbersome in the beginning but on second attempt - i realized that i need to use the info in the way they have given it

let F% be discount rate on Fox and P% be discount rate on Pony
Then, F+P=22 ---equation 1
Also, 3(F%(15))+2(P%(18))=9 ----equation 2
equation 1 is just the sum of the two discount rates
equation 2 is discount rate on each item, multiplied by the number of items purchased = total amount of the discount
when I try to solve the two equations, through substitution or simultaneously, I get a weird answer.
can some one please tell me where I messed up?

[kvcpk]

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%


seemed cumbersome in the beginning but on second attempt - i realized that i need to use the info in the way they have given it

let F% be discount rate on Fox and P% be discount rate on Pony
Then, F+P=22 ---equation 1
Also, 3(F%(15))+2(P%(18))=9 ----equation 2
equation 1 is just the sum of the two discount rates
equation 2 is discount rate on each item, multiplied by the number of items purchased = total amount of the discount
when I try to solve the two equations, through substitution or simultaneously, I get a weird answer.
can some one please tell me where I messed up?

Your equations are correct. I think your calculations are wrong.
45f%+36P%=9
45f+36p=900
f+p=22
45f+45p=990
9p=90
p=10

[Rahul@gurome]

After discount the price is F% of 3($15) + P% of 2($18) = $9
45F/100 + 36P/100 = 9 or 45F + 36P = 900
Also F + P = 22 or 45F + 45P = 990
solving the two equations we get, 9P = 90 or P = 10

The correct answer is (B).

[GMATGuruNY]

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%

Another approach -- especially if you're not good with equations -- would be to use the answers choices, which represent the discount rate on P.

First let's determine how much it would cost to buy the jeans without the discounts:
F = 3*15 = 45.
P = 2*18 = 36.

Now let's see which answer choice will give us a total savings of $9.

Answer choice C is too obvious because the problem states that the sum of the discount rates is 22, and 1/2 * 22 = 11.

Let's try B, which says that the discount on P is 10%, which means the discount on F would be 22-10=12%.

Discount on P would be (10/100) * 36 = 3.6
Discount on F would be (12/100) * 45 = 5.4

3.6 + 5.4 = 9. Success! The total discount is $9.

The correct answer is B.

[san2009]

i like the backsolving method as well.
thank you!!