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A student spent 60% of her money on books and spent 1/3 of the remaind

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A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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New post 12 Jul 2019, 09:12
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:41) correct 21% (01:51) wrong based on 43 sessions

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A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had $30 left. How much money did the student have at first?

A)225
B)167.5
C) 68.2
D) 245
E) 112.5

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A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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New post 13 Jul 2019, 00:54
1
GeorgeKo111 wrote:
A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had $30 left. How much money did the student have at first?

A)225
B)167.5
C) 68.2
D) 245
E) 112.5



Let's look at the question stem:
1. Assume she had x$
2. 0.6x spent on books => 0.4x left
3. 0.4x * 1/3 spent on notebooks => 0.4x*2/3 left which is 30$
4. Let's then get back => x=30 / 0.4 / (2/3) = 112.5$

Answer E

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Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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New post 13 Jul 2019, 01:46
Let's assume the student had $x at the start.
She spent 60% on books
=> Remainder = x - 0.6x = 0.4x

She spent 1/3 of this on notebooks
=> Remainder = 0.4x - (1/3)(0.4x) = 0.8x/3

Given then 0.8x/3 = 30
=> x = (30*3)/0.8 = 112.5

The answer is (E).
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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New post 08 Aug 2019, 11:20
Let's assume the student had 100$ initially.
60$-spent on books; Remaining 40$;
1/3(40$)-spent on notebooks;2/3(40$)-left amount;
for 100$, 2/3(40$)is left. So, if 30$ is left then initial amount can be calculated

100=>2/3(40$)
x=>30$left; cross multiply(30*100)/(80/3)=9000/80=112.5$
option E
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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New post 08 Aug 2019, 20:20
1
Out of the initial x dollars.
40% is left.
Out of that 40 %, 1/3 is spent on notebooks, 2/3 is the remainder which is given as 30 $.
So, 2/3* 40%*x = 30.
x = 112.5
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind   [#permalink] 08 Aug 2019, 20:20
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