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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
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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:

90% (01:29) correct 10% (02:45) wrong based on 50 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
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

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.

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Re: Susan spent one-third of her money on books and half of the remaining &nbs [#permalink] 30 Oct 2018, 18:11
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