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Pens cost 70 cents each and pencils cost 40 cents each. If I

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Pens cost 70 cents each and pencils cost 40 cents each. If I [#permalink] New post 14 Jun 2018, 14:05
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Question Stats:

100% (00:29) correct 0% (00:00) wrong based on 3 sessions
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
[Reveal] Spoiler: OA

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1664 [0], given: 396

CAT Tests
Re: Pens cost 70 cents each and pencils cost 40 cents each. If I [#permalink] New post 05 Jul 2018, 01:32
Expert's post
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!
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Re: Pens cost 70 cents each and pencils cost 40 cents each. If I   [#permalink] 05 Jul 2018, 01:32
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Pens cost 70 cents each and pencils cost 40 cents each. If I

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