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# Susan spent one-third of her money on books and half of the remaining

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Math Expert
Joined: 02 Sep 2009
Posts: 64144
Susan spent one-third of her money on books and half of the remaining  [#permalink]

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29 Oct 2018, 06:11
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Difficulty:

15% (low)

Question Stats:

86% (01:58) correct 14% (02:32) wrong based on 70 sessions

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Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with? A.$60
B. $80 C.$120
D. $160 E.$180

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Re: Susan spent one-third of her money on books and half of the remaining  [#permalink]

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29 Oct 2018, 07:29
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Bunuel wrote:
Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with? A.$60
B. $80 C.$120
D. $160 E.$180

Let the amount of money she had be 12x

Amount spent on books = 4x
Amount spent on clothing = 4x
Amount spent on food = 3x
Amount left = x = $5 So, the total amount of money she had is$ 60, Answer must be (A)
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Re: Susan spent one-third of her money on books and half of the remaining  [#permalink]

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30 Oct 2018, 02:28

Solution

Given:
• Susan spent
o $$\frac{1}{3}^{rd}$$ of her money on books,
o $$\frac{1}{3}^{rd}$$on clothing
o $$\frac{1}{4}^{th}$$ on food

• She had $5 left over To find: • The total money she had at the beginning Approach and Working: • Let the initial amount be$X
• Left over money = $$(1 - \frac{1}{3} - \frac{1}{3} - \frac{1}{4}) * X = 5$$
o Implies, X = $5 * 12 =$60

Hence, the correct answer is Option A

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Re: Susan spent one-third of her money on books and half of the remaining  [#permalink]

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30 Oct 2018, 18:11
1
Bunuel wrote:
Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with? A.$60
B. $80 C.$120
D. $160 E.$180

We can let the total amount of money Susan had = n.

So she spent n/3 on books, (1/2)(n - n/3) = (1/2)(2n/3) = n/3 on clothing and (3/4)(n - n/3 - n/3) = (3/4)(n/3) = n/4 on food. We can create the equation:

n/3 + n/3 + n/4 + 5 = n

Multiplying the equation by 12, we have:

4n + 4n + 3n + 60 = 12n

11n + 60 = 12n

60 = n

So she had $60 before she spent it on books, clothing and food. Answer: A _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 202 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern Joined: 28 Jan 2020 Posts: 4 Re: Susan spent one-third of her money on books and half of the remaining [#permalink] ### Show Tags 15 Mar 2020, 02:54 Abhishek009 wrote: Bunuel wrote: Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had$5 left over. How much money did she start with?

A. $60 B.$80
C. $120 D.$160
E. $180 Let the amount of money she had be 12x Amount spent on books = 4x Amount spent on clothing = 4x Amount spent on food = 3x Amount left = x =$5

So, the total amount of money she had is $60, Answer must be (A) Please how did your get your 60, from your calculations there is really no way x=$5
will turn to 60
what am i missing

Re: Susan spent one-third of her money on books and half of the remaining   [#permalink] 15 Mar 2020, 02:54