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Pens cost 70 cents each and pencils cost 40 cents each. If I
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14 Jun 2018, 14:05
14 Jun 2018, 14:05
Expert Reply
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Question Stats:
88% (01:47) correct
11% (02:28) wrong based on 42 sessions
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Pens cost 70 cents each and pencils cost 40 cents each. If Iris spent $5.20 on a total of 10 pens and pencils, how many pencils did she purchase? ($1 = 100 cents)
(A) 4
(B) 6
(C) 8
(D) 10
(E) 13
(A) 4
(B) 6
(C) 8
(D) 10
(E) 13
Re: Pens cost 70 cents each and pencils cost 40 cents each. If I
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05 Jul 2018, 01:32
05 Jul 2018, 01:32
Expert Reply
Explanation
Assign one variable to the pencils and another variable to the pens:
Number of pencils = x
Number of pens = y
\(x + y = 10\)
\(70y + 40x = 520\)
The question asks for the number of pencils, x, so isolate y in the first equation and substitute into the second:
\(y = 10 - x\)
\(70(10 - x) + 40x = 520\)
\(700 - 70x + 40x = 520\)
\(700 - 30x = 520\)
\(180 = 30x\)
\(x = 6\)
Alternatively, test the answer choices. Starting with the middle choice, if Iris bought 8 pencils and therefore 2 pens, she spent (8 × 40) + (2 × 70) = 320 + 140 = 460. That’s 60 cents too little, so Iris must have bought fewer pencils and more pens. Try 6 pencils and 4 pens: (6 × 40) + (4 × 70) = 240 + 280 = 520. (You might also have noticed that every time Iris swaps a pencil for a pen, she spends an extra 30 cents.)
Hence option B is correct!
Assign one variable to the pencils and another variable to the pens:
Number of pencils = x
Number of pens = y
\(x + y = 10\)
\(70y + 40x = 520\)
The question asks for the number of pencils, x, so isolate y in the first equation and substitute into the second:
\(y = 10 - x\)
\(70(10 - x) + 40x = 520\)
\(700 - 70x + 40x = 520\)
\(700 - 30x = 520\)
\(180 = 30x\)
\(x = 6\)
Alternatively, test the answer choices. Starting with the middle choice, if Iris bought 8 pencils and therefore 2 pens, she spent (8 × 40) + (2 × 70) = 320 + 140 = 460. That’s 60 cents too little, so Iris must have bought fewer pencils and more pens. Try 6 pencils and 4 pens: (6 × 40) + (4 × 70) = 240 + 280 = 520. (You might also have noticed that every time Iris swaps a pencil for a pen, she spends an extra 30 cents.)
Hence option B is correct!
gmatclubot
Re: Pens cost 70 cents each and pencils cost 40 cents each. If I [#permalink]
05 Jul 2018, 01:32
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