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

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by Gmat_mission » Sat Mar 17, 2018 8:59 am
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

[spoiler]OA=B[/spoiler].

I am confused. What are the equations that I should set here? Can any expert give me some help? Thanks in advanced.
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by [email protected] » Sat Mar 17, 2018 6:57 pm
Hi Gmat_mission,

We're told that John spent 3/5 of his allowance at the arcade, then spent one third of his remaining allowance at the toy store and then spent his last $0.80 at the candy store. We're asked for John's weekly allowance. This question can be solved by TESTing THE ANSWERS.

Let's start with the 'easiest' answer and TEST Answer B first:

Answer B: $3.00
IF.... John's allowance = $3.00
He spent (3/5)($3) at the arcade = $1.80 spent at the arcade, leaving $3.00 - $1.80 = $1.20
He then spent (1/3)($1.20) at the toy store = $0.40 spent at the toy store, leaving $1.20 - $0.40 = $0.80
This is an exact match for what we were told, so this must be the answer.

Final Answer: B

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

by Brent@GMATPrepNow » Sun Mar 18, 2018 6:29 am
Gmat_mission 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
Let w = John's weekly allowance

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade
If John spent 3/5 of his allowance, then he has 2/5 REMAINING
So, (2/5)(w) = allowance REMAINING

The next day he spent one third of his remaining allowance at the toy store
If he spent 1/3, then he has 2/3 REMAINING
So, (2/3)(2/5)(w) = allowance REMAINING

Once all of this is done, John had $0.80 REMAINING
So (2/3)(2/5)(w) = 0.8
Simplify: (4/15)(w) = 0.8
Multiply both sides by 15 to get: 4w = 12
Divide both sides by 4 to get: w = 3

Answer: B

Cheers,
Brent
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by Jeff@TargetTestPrep » Wed Mar 21, 2018 3:25 pm
Gmat_mission 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
We can let n = the weekly allowance and create the equation:

(3/5)n + 1/3(2/5)n + 0.8 = n

3n/5 + 2n/15 + 0.8 = n

Multiplying by 15, we have:

9n + 2n + 12 = 15n

12 = 4n

3 = n

Answer: B

Jeffrey Miller
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by Gmat_mission » Sat Mar 24, 2018 4:39 am
I'm really thankful for all your answers.
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