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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] New post   02 Dec 2021, 05:00
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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. 245
B. 225
C. 167.5
D. 112.5
E. 68.2
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D
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind [#permalink] New post   26 Dec 2021, 10:52
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Given: A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had $30 left.
Asked: How much money did the student have at first?

Let the student have $x initially.
A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had $30 left.

A student spent 60% of her money on books
The remainder = x - 60%x = 40%x
She spent 1/3 of the remainder on notebooks.
The money left after spendings = 40%x (1 - 1/3) = (2/3)*40%x = $30
x = 90/.8 = 900/8 = $112.5

IMO D
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind [#permalink] New post   26 Dec 2021, 15:25
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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. 245
B. 225
C. 167.5
D. 112.5
E. 68.2

Solution:

Let the amount of money the student had initially be x.

For books he spent: 0.6x
For notebook: 1/3 (0.4x)

Remaining = 2/3 (0.4x) = 30$
or, x = 90/0.8 = 112.5$

Answer: D
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind [#permalink] New post   26 Dec 2021, 18:55
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remainign 1/3rd is => 40% of (2/3)X = 30$
that gives X= 90/.8 = 450/4 = 112.5

D
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Re: A student spent 60% of her money on books and spent 1/3 of the remaind [#permalink]
26 Dec 2021, 18:55
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