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A customer buys two products, X and Y, and spends a total of $350

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A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 08 Oct 2018, 12:22
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Difficulty:

  15% (low)

Question Stats:

90% (02:20) correct 10% (02:27) wrong based on 60 sessions

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A customer buys two products, X and Y, and spends a total of $350. Both products come with rebate coupons. The rebate on the price of product X is 15 percent, and the rebate on the price of product Y is 10 percent. If x and y are the prices of products X and Y, respectively, before the rebate and the total rebate earned by the customer was $45, how much did each product cost?
A) x = $200, y = $150
B)x= $130, y = $220
C) x= $140, y = $210
D x = $300, y = $50
E)x = $175, y = $175

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Re: A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 08 Oct 2018, 15:05
Abhi077 wrote:
A customer buys two products, X and Y, and spends a total of $350. Both products come with rebate coupons. The rebate on the price of product X is 15 percent, and the rebate on the price of product Y is 10 percent. If x and y are the prices of products X and Y, respectively, before the rebate and the total rebate earned by the customer was $45, how much did each product cost?
A) x = $200, y = $150
B)x= $130, y = $220
C) x= $140, y = $210
D x = $300, y = $50
E)x = $175, y = $175


x*(15/100) + y (10/100) = 45

15x + 10y = 4,500 (1)

x + y = 350
10x + 10y = 3,500 (2)

(1) - (2)
5x = 1,000
x = 200

Only answer A has x as 200.



You can do it as back solving also

200*(15/100) = 30
150*(10/100) = 15

30 + 15 = 45

Posted from my mobile device
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Re: A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 10 Nov 2018, 06:33
Salsanousi wrote:
Abhi077 wrote:
A customer buys two products, X and Y, and spends a total of $350. Both products come with rebate coupons. The rebate on the price of product X is 15 percent, and the rebate on the price of product Y is 10 percent. If x and y are the prices of products X and Y, respectively, before the rebate and the total rebate earned by the customer was $45, how much did each product cost?
A) x = $200, y = $150
B)x= $130, y = $220
C) x= $140, y = $210
D x = $300, y = $50
E)x = $175, y = $175


x*(15/100) + y (10/100) = 45

15x + 10y = 4,500 (1)

x + y = 350
10x + 10y = 3,500 (2)

(1) - (2)
5x = 1,000
x = 200

Only answer A has x as 200.



You can do it as back solving also

200*(15/100) = 30
150*(10/100) = 15

30 + 15 = 45

Posted from my mobile device


Hi Salsanousi,

if x and y are the prices of the two products before the rebate , then shouldn't x + y = 395 ?
because total rebate is 45 and after the rebate 350 was paid .

and .85x + .90y= 350 ( This should be the price after the rebate IMO)
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Re: A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 24 Nov 2018, 14:49
I think this question is wrong, the value 350 in the question should have been 305

It should be like this instead.

0.85x + 0.9y = 305

and

0.15x + 0.9y = 45

solving the two equations will give us

x = 200 and y = 150
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A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 16 Jan 2019, 18:18
muus wrote:
I think this question is wrong, the value 350 in the question should have been 305

It should be like this instead.

0.85x + 0.9y = 305

and

0.15x + 0.9y = 45

solving the two equations will give us

x = 200 and y = 150



\(\frac{85}{100}x+ \frac{90}{100}y=350 (1)\)
\(\frac{15}{100}x+ \frac{10}{100}y=45 (2)\)

Further simplification of (1)
85x + 90y=35000 -> 17x + 18y=7000
Further simplification of (2)
15x+10y=4500-> 3x+2y=900

So final two equations are
17x + 18y=7000
3x+2y=900

On solving these I am getting x =110 and y=255

Please let me know if I am making any mistake anywhere.Thank you.
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A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 17 Jan 2019, 00:15
What is the question source?


Incorrect answers are from not understanding what a rebate coupon is. Think of it like a little card with your product. After you pay FULL PRICE, you send that little card to the manufacturer and they send back the rebate.

Essentially, it relies on the laziness of consumers for bonus money, rather than offering an upfront lower price.

x+y=350

15/100x+10/100y=45, 15x+10y=4500, 3x+2y=900


x+y=350
2x+2y=700

3x+2y=900
-(2x+2y=700)
x=200

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Re: A customer buys two products, X and Y, and spends a total of $350  [#permalink]

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New post 17 Jan 2019, 00:39
Abhi077 wrote:
A customer buys two products, X and Y, and spends a total of $350. Both products come with rebate coupons. The rebate on the price of product X is 15 percent, and the rebate on the price of product Y is 10 percent. If x and y are the prices of products X and Y, respectively, before the rebate and the total rebate earned by the customer was $45, how much did each product cost?
A) x = $200, y = $150
B)x= $130, y = $220
C) x= $140, y = $210
D x = $300, y = $50
E)x = $175, y = $175


Total rebate = 45
This means that=> 350 - x = 45
After rebate the value was 305

Out of the answer options
which value when used in the equation 0.85 x + 0.90 y = 305

If you are comfortable with multiplication under time pressure, only A satisfies the above equation.
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Re: A customer buys two products, X and Y, and spends a total of $350   [#permalink] 17 Jan 2019, 00:39
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A customer buys two products, X and Y, and spends a total of $350

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