Simple question re discounts

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caspermonday: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Fri Aug 14, 2009 12:03 am

Simple question re discounts

by caspermonday » Wed Oct 21, 2009 9:57 am

It's a shame to post such a simple question, but I am definitely mistaken somewhere in my calculations, could anyone help?

Fox jeans sell for USD 15
Pony jeans sell for USD 18

During a sale the two types of jeans are discounted at different rates so that you save USD 9 if you purhcase 3 pairs of Fox and 2 pairs of Pony.

Sum of the two discount rates is 22%.

What is the discount on Pony jeans?

OA [spoiler]10%[/spoiler]

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Source: Beat The GMAT — Problem Solving | Wed Oct 21, 2009 9:57 am

briantime: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Oct 18, 2009 3:39 am; Location: Baden-Baden, Germany; Thanked: 2 times; Followed by:1 members; GMAT Score:690

Re: Simple question re discounts

by briantime » Wed Oct 21, 2009 12:16 pm

Hi caspermonday,

We are given the following:
f = price for fox jeans = 15
p = price for pony jeans = 18
x = discount for fox jeans in percent
y = discount for pony jeans in percent

x + y = 22
or: x = 22 - y

As a fraction:
x/100 + y/100 = 22/100

From the information we can derive:
3*(15-(x/100)*15) + 2(18-(y/100)*18) = 72 // because 3*15+2*18-9 = 72
Simplify:
45 - 45x/100 + 36 -36y/100 = 72
1 = 5x/100 + 4y/100
100 = 5x + 4y

Since x = 22 - y:

100 = 5(22-y) + 4y
100 = 110 - 5y + 4y
y = 10

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

Re: Simple question re discounts

by ssuarezo » Wed Oct 21, 2009 8:22 pm

briantime wrote:Hi caspermonday,

We are given the following:
f = price for fox jeans = 15
p = price for pony jeans = 18
x = discount for fox jeans in percent
y = discount for pony jeans in percent

x + y = 22
or: x = 22 - y

As a fraction:
x/100 + y/100 = 22/100

From the information we can derive:
3*(15-(x/100)*15) + 2(18-(y/100)*18) = 72 // because 3*15+2*18-9 = 72
Simplify:
45 - 45x/100 + 36 -36y/100 = 72
1 = 5x/100 + 4y/100
100 = 5x + 4y

Since x = 22 - y:

100 = 5(22-y) + 4y
100 = 110 - 5y + 4y
y = 10

Hi Brian:

Why didn't you use x=22/100 - y? .. in your previous equations you divide the rate by 100 (3*(15-(x/100)*15) + 2(18-(y/100)*18) = 72). What is the OA?

Silvia

Sorry !! .. I've already understood that u simplified x/100 = 22/100 - y/100 ... Thank you !

Silvia again

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uttam.albela: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Fri Aug 28, 2009 2:40 am; Location: Singapore; Thanked: 11 times

by uttam.albela » Wed Oct 21, 2009 9:11 pm

as we have to find discount on pony jeans, assume discount to be x

Discount on fox = 22-x

Discount 1 + Discount 2 = 9

[15 * 3 * (22-x)/100] + [18 * 4 * x/100] = 9

Solve this to get x = 10

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briantime: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Oct 18, 2009 3:39 am; Location: Baden-Baden, Germany; Thanked: 2 times; Followed by:1 members; GMAT Score:690