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# Marcy bought one pair of jeans at 70% off and one blouse at

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Marcy bought one pair of jeans at 70% off and one blouse at [#permalink]  14 Jun 2018, 14:17
Expert's post
00:00

Question Stats:

25% (01:17) correct 75% (00:31) wrong based on 4 sessions
Marcy bought one pair of jeans at 70% off and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans, and she spent a total of$84, what was the original price of the jeans?

(A) 76
(B) 96
(C) 100
(D) 120
(E) 124
[Reveal] Spoiler: OA

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Sandy
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Joined: 20 Apr 2016
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Re: Marcy bought one pair of jeans at 70% off and one blouse at [#permalink]  03 Jul 2018, 05:23
1
KUDOS
sandy wrote:
Marcy bought one pair of jeans at 70% off and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans, and she spent a total of$84, what was the original price of the jeans?

(A) 76
(B) 96
(C) 100
(D) 120
(E) 124

For easy calculation let us take the price of the discounted jeans = X

and price of the discounted blouse = Y

so we can write as

Y = X + 12

and X + Y = 84

or X + (X +12) = 84

or X = 36

Now the discounted price = original price * (100% - discount percent)

or X = Original Price * 0.3

or 36 = 0.3 * original price

or original price = 120
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: Marcy bought one pair of jeans at 70% off and one blouse at [#permalink]  05 Jul 2018, 02:55
Expert's post
Explanation

To solve this problem, establish the following variables:

J = original jean price

B = original blouse price

Next, establish a system of equations, keeping in mind that “70% off” is the same as 100% – 70% = 30%, or 0.3, of the original price:

$$0.3J + 12 = 0.6B$$

$$0.3J + 0.6B = 84$$

Now use whatever strategy you’re most comfortable with to solve a system of equations—for example, aligning the equations and then subtracting them:

$$0.3J + 12 = 0.6B$$

$$0.3J - 84= -0.6B$$

-----------------------------
$$0 +96=1.2B$$

$$B=80$$

You can plug the price of the blouse back into the original equation to get the price of the jeans:

$$0.3J + 12 = 0.6B$$

$$0.3J + 12 = 48$$

$$0.3J = 36$$

$$J = 120$$

Alternatively, you could first figure out the price of the discounted jeans, x, with this equation:

$$x + (x + 12) = 84$$

$$2x + 12 = 84$$

$$2x = 72$$

$$x = 36$$

Then plug that discounted price into the equation discounted price = original price × (100% – percent discount):

$$36 = 0.3P$$

$$360 = 3P$$

$$120 = P$$

Hence option D is correct!
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Sandy
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Re: Marcy bought one pair of jeans at 70% off and one blouse at   [#permalink] 05 Jul 2018, 02:55
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