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Fox jeans regularly sell for $15 a pair and pony jeans

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Fox jeans regularly sell for $15 a pair and pony jeans [#permalink] New post 03 Sep 2006, 11:01
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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 pair of jean: 3 pairs of Fox and 2 pairs of Pony jeans. If the sume 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%
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 [#permalink] New post 03 Sep 2006, 13:18
Looks like the only way to do it is to plug in the numbers (e.g. Fox total undiscounted is $45, Pony total undiscounted is $36. Then if Pony is 9% off, Fox is 13% off, calculated the discounted totals, subtract them from the original, check if the diffferences add up to 9). B is the answer so it can be done in under 2 minutes if you can multiply and substract fast.

I suspect there is more eklegant solution using the derivatives but can't find it
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 [#permalink] New post 03 Sep 2006, 16:02
Got B

An easier was to look at this prob. would be to say average discount per jean = 9/5 = $1.80

Now 1.8 is 10% of pony and testing with 12% for fox gives you the answer
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 [#permalink] New post 03 Sep 2006, 23:08
before discount:
45$ were spent on Fox and 36$ were spent on pony.
say discount on fox = x% then discount on pony = 22-x

=> 45x/100 + 36(22-x)/100 = 9

=> x = 12

so discount on pony = 22-12 = 10%

Last edited by iced_tea on 03 Sep 2006, 23:17, edited 1 time in total.
  [#permalink] 03 Sep 2006, 23:08
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