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08 Oct 2018, 12:22
1
2
00:00

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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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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- Stne
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Joined: 04 Nov 2017
Posts: 11

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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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- Stne
Senior Manager
Joined: 15 Feb 2018
Posts: 257

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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 Display posts from previous: Sort by # A customer buys two products, X and Y, and spends a total of$350

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