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Marcy bought one pair of jeans at 70% off and one blouse at
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14 Jun 2018, 14:17
14 Jun 2018, 14:17
Expert Reply
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Question Stats:
82% (02:03) correct
17% (01:52) wrong based on 41 sessions
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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
(A) 76
(B) 96
(C) 100
(D) 120
(E) 124
Re: Marcy bought one pair of jeans at 70% off and one blouse at
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03 Jul 2018, 05:23
03 Jul 2018, 05:23
3
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
(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
Re: Marcy bought one pair of jeans at 70% off and one blouse at
[#permalink]
05 Jul 2018, 02:55
05 Jul 2018, 02:55
1
Expert Reply
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!
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!
