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Having received his weekly allowance, John spent 3/5 of his

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Having received his weekly allowance, John spent 3/5 of his [#permalink]

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New post 18 Oct 2010, 09:50
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Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

A. 2.40
B. 3.00
C. 3.20
D. 3.60
E. 4.80

it's relatively an easy question but what i am interested in is, if this question has to be solve through Plug in or back solving method as the answer choices have fractions......
[Reveal] Spoiler: OA

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Re: back solving [#permalink]

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New post 18 Oct 2010, 09:58
i guess my method is more backsolving.

lets say his allowance is x.
x = allowance
3x/5 = allowance on arcade
this must mean that there is 2x/5 remaining

1/3(2x/5) = toy store => 2x/15 = toy store

adding 3/5 and 2/15 we get a total amount spent of 11x/15 of his allowances. this must mean that there is only 4x/15 remaining. since his last bit of money was .80, we can say 4x/15 = .80. solving for x we have x = $3.00

i think backsolving would be easier than plug in. i find it more beneficial to plug in when there are variables in the question AND answer choices.
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Re: back solving [#permalink]

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New post 18 Oct 2010, 10:08
Isn't it algebraic ? ( may be i'm confused with back solving and plug in )
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Re: back solving [#permalink]

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New post 18 Oct 2010, 16:51
shrive555 wrote:
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

2.40

3.00

3.20

3.60

4.80

it's relatively an easy question but what i am interested in is, if this question has to be solve through Plug in or back solving method as the answer choices have fractions......


When you backsolve, just ignore the decimals. For example, 3.20 = 320 cents.
Since after spending 3/5 and 1/3, John spends his last 80 cents, the correct answer must be divisible by 5 and 3. Eliminate C.

Answer choice B: allowance = 300
Spends 3/5, means (2/5)*300 = 120 left.
Spends 1/3, means (2/3)*120 = 80 left.
This works.

The correct answer is B.
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Re: Having received his weekly allowance, John spent 3/5 of his [#permalink]

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New post 07 Jan 2014, 04:06
shrive555 wrote:
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

A. 2.40
B. 3.00
C. 3.20
D. 3.60
E. 4.80

it's relatively an easy question but what i am interested in is, if this question has to be solve through Plug in or back solving method as the answer choices have fractions......


Let us back solve here. Lets start with C (Always start with C)
Allowance.....Arcade......Remaining.....Toy Store.....Remaining
A. 2.40
B. 3.00
C. 3.20.........1.92.........1.28..............1.28/3 - Weird number
D. 3.60.........................1.44..............0.48..............0.96 - we were supposed to get 0.80 however we got a bigger number so move up
E. 4.80


A. 2.40
B. 3.00.........................1.2.................4.................0.8 (BINGO)
C. 3.20.........1.92.........1.28..............1.28/3 - Weird number
D. 3.60.........................1.44..............0.48..............0.96 - we were supposed to get 0.80 however we got a bigger number so move up
E. 4.80

Hence our answer is B
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Re: Having received his weekly allowance, John spent 3/5 of his [#permalink]

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New post 27 Oct 2015, 21:36
shrive555 wrote:
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

A. 2.40
B. 3.00
C. 3.20
D. 3.60
E. 4.80

it's relatively an easy question but what i am interested in is, if this question has to be solve through Plug in or back solving method as the answer choices have fractions......



Posting how I did this because I think it was harder then the other lower level question . Seems more middle of the pack to me. 600-700

Anyways

Solution

Let X be the allowance

Arcade - 3/5X ..... 2/5X Left

Toy Store 1/3 of amount left = 2/5x = 2/15x <-- spent at toy store

Amount left after the Toy Store 2/5x-2/15x = 4/15x

He has 4/15x left for his allowance and this = to 0.80

4/15x=0.80
x=15*0.2
x=3.00
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Re: Having received his weekly allowance, John spent 3/5 of his [#permalink]

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New post 23 Jan 2016, 14:36
let a=allowance
.8=(2/3)(2/5)a
a=.8/(4/15)=$3.00
Re: Having received his weekly allowance, John spent 3/5 of his   [#permalink] 23 Jan 2016, 14:36
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