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best method?

by mehaksal » Sat Aug 25, 2012 4:59 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 two discounts rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%

what's the best method of solving this question??
answer given : B
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by neelgandham » Sat Aug 25, 2012 5:30 am
Let the discount on Fox jeans be F% and the discount on Pony jeans be P%

Original cost of 3 pairs of Fox jeans and 2 pairs of Pony jeans = 3*15 + 2*18 = $81
Discounted price of one pair of Fox jeans = 15 - (F/100)*15
Discounted price of one pair of Pony jeans = 18 - (P/100)*18
Discounted cost of 3 pairs of Fox jeans and 2 pairs of Pony jeans = 3*(15 - (F/100)*15) + 2*(18 - (P/100)*18)

It is also given that (Original cost of 3 pairs of Fox jeans and 2 pairs of Pony jeans) - (Discounted cost of 3 pairs of Fox jeans and 2 pairs of Pony jeans) = $9
i.e. 3*15 + 2*18 - 3*15 + 3*(F/100)*15 + 2*18 + 2*(P/100)*18 = $9
45F + 36P = 900
5F + 4P = 100 - Equation 1
It is also given that
F + P = 22 - Equation 2

5*(Equation 2) - Equation 1, gives
5F + 5P - 5F - 4P = 110 - 100
P = discount on Pony jeans = 10%
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by adthedaddy » Sat Aug 25, 2012 5:54 am
Following method may seem simple.

With 3 qty of Fox and 2 Qty of Pony jeans, the Orig price is 3*15 + 2*18 = 45 + 36 = 81

Let the discounts on Fox & Pony jeans be x% and y% respectively. Discount is $9.

Thus we can form an eqn as -

45x% + 36y% = $9
i.e. 45x/100 + 36y/100 = 9
i.e. 45x + 36y = 900
i.e. 5x + 4y = 100 ............. (1)
Also, x + y = 22 (given in the question)..........(2)

Solving (1) and (2),
We get y=10

Thus, ans = Option B
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