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A credit card company has a cash back option for their customers which

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A credit card company has a cash back option for their customers which [#permalink]

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New post 15 Feb 2015, 15:37
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A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10000. If a customer receives a cash back of 2.6% on their total annual charges made on the credit card, then what was the customer's annual charge?

1. 22,500

2. 23,500

3. 25,000

4. 26,000

5. 26,500
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A credit card company has a cash back option for their customers which [#permalink]

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hi Turkish,

take the amount at 3% be x..
so total= 1.5*5000 +2.5*5000+3*x =2.6(10000+x)..
7500+12500+3x = 26000 + 2.6x...
.4x=6000... or x = 15000..
so annual charge=10000+15000=25000
ans C..
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Re: A credit card company has a cash back option for their customers which [#permalink]

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New post 15 Feb 2015, 22:22
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Turkish wrote:
A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10000. If a customer receives a cash back of 2.6% on their total annual charges made on the credit card, then what was the customer's annual charge?

1. 22,500

2. 23,500

3. 25,000

4. 26,000

5. 26,500


Note that cash back is 1.5% on first $5000 and 2.5% on next $5000 so overall, cashback is 2% on first $10,000. Since the customer receives 2.6% cashback, his expenses were much more than $10,000. Now simply use weighted average to get the ratio of expenses upto 10,000 and more than 10,000:

w1/w2 = (3 - 2.6)/(2.6 - 2) = 2/3
So first 10,000 is 2 parts out of 2+3 = 5 parts of his total expense. So 10,000 = (2/5) * Total expense
Total expense = $25,000
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Re: A credit card company has a cash back option for their customers which [#permalink]

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New post 14 Nov 2015, 12:54
i back solved it by picking numbers from answer choices:
C: 25k total charge
that means 15k will be cash back with 3% or 450 total $ cash back
on first 10k will be 200 $ cash back. So total cash back would be 650$
650/25,000 - 65/2500 divide by 5 = 13/500 multiply by 2 = 26/1000 or 2.6%
C.

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Re: A credit card company has a cash back option for their customers which [#permalink]

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New post 17 Feb 2016, 09:23
Let T be the total spent.

Customer earns $200 on first $10k. So, the total cash back equals:

$200 + .03(T - 10k) = .026T.

$200 + .03T - 300 = .026T

.03T = .026T + 100

.004T = 100.

T = 25k.

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Re: A credit card company has a cash back option for their customers which   [#permalink] 28 Dec 2017, 12:14
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