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

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

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New post 29 Oct 2018, 07:11
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

91% (01:53) correct 9% (03:26) wrong based on 54 sessions

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

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New post 29 Oct 2018, 08:29
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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New post 30 Oct 2018, 03:28

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

Answer: 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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New post 30 Oct 2018, 19:11
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
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Re: Susan spent one-third of her money on books and half of the remaining   [#permalink] 30 Oct 2018, 19:11
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