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

Question

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

Kudos for a correct solution.

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

GSBae · Accepted Answer

Let's take a look at how much John spent. Let his allowance be A.

Arcade: 3/5 * A
Toy Store: 1/3 of his remaining allowance. This means he spent (1/3)*(2/5)*A.
Candy Store: .8

The total amount spent has to add up to his allowance. Thus,

\frac{3}{5}*A + \frac{1}{3}*\frac{2}{5}*A + .8 = A

\frac{3}{5}*A + \frac{2}{15}*A + .8 = A

\frac{9}{15} A + \frac{2}{15} A + .8 = A

\frac{11}{15}A + .8 = A

.8 = \frac{4}{5} = \frac{4}{15} A.

A = \frac{4}{5}*\frac{15}{4} = \frac{15}{5} = 3.

Therefore, John's total allowance is 3 dollars.

Answer: B

BrentGMATPrepNow · Answer

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 has $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

sanchito · Answer

Let A be John's total weekly allowance.

(3/5)A went to Arcade

"The next day he spent one third of his remaining allowance at the toy store"
This is the tricky part because if you don't read the stem well, you will assume that 1/3(A) is spent on the toy store.

Rather, he spent the 1/3 of his  remaining allowance , which is 1/3 of (2/5)A or (2/15)A

"and then spent his last $0.80 at the candy store"
A -  = A - (11/15)A = (4/15)A

Therefore (4/15)A = .80 or 4/5 cents

A = $3.00

ngie · Answer

Allowance:  x

x=\frac{3}{5}x+\frac{1}{3}(1-\frac{3}{5})x+0.8 
 \frac{2}{5}x=\frac{1}{3}\frac{2}{5}+0.8 
 \frac{6-2}{15}x=0.8\Rightarrow x=\frac{15\cdot 0.8}{4}=3

The correct answer is B

PareshGmat · Answer

Answer = B = 3

Let the opening balance = x (Salary)

Spent at arcade =  \frac{3x}{5} ; Balance =  \frac{2x}{5}

Spent at toy store  = \frac{2x}{5} * \frac{1}{3} = \frac{2x}{15} ; Balance =  \frac{4x}{15}

Given that the final balance  \frac{4x}{15} = 0.80

x = 3

earnit · Answer

Let the initial amount be x.

He spends 3/5 of it. that leaves (2/5)*x

He spends 1/3rd of (2/5)*x that leaves him with 2/3rd of (2/5)*x.

It is mentioned that he has $0.8 remaining. 
So  (2/3)*(2/5)*x = 0.8 
 x = 3.

Answer:  B

KS15 · Answer

Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.8
Therefore, X=$3.00. Answer B

EMPOWERgmatRichC · Answer

Hi All,

Since this question asks for John's weekly allowance, and the answers are numbers, we can TEST THE ANSWERS.

Normally, when TESTing THE ANSWERS, it's best to start with Answer B or Answer D. Answer B looks like the easier answer to work with, so we'll start there...

IF....John's allowance is $3....

First, John spent 3/5 of his allowance at the arcade....

(3/5)($3) = $1.80

$3 - $1.80 = $1.20

Next, John spends 1/3 of his remaining allowance at the toy store...

(1/3)($1.20) = $0.40

$1.20 - $0.40 = $0.80

Then he spent his last 80 cents at the candy store....

In Answer B, John is left with 80 cents for the last "step", so this MUST be the answer.

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Celerma · Answer

3x/5 + (x-3x/5)/3 + 0.8 = x, Solving for x , x= 3

Answer is  B

dream21 · Answer

Let Allowance be x

x- (3/5x + 1/3(2/5x)) = 0.8

X= 3

Ans B

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

We know the following:
1. John spent 3/5 of his allowance at the arcade
2. The next day, John spent 1/3 of his remaining allowance at the toy store
3. Then he spent the remaining $0.80 at the candy store.

Let's set John's allowance to A.

Day One:  John spent (3/5)A.

This means he has A - (3/5)A in his pocket. That's (2/5)A.

Day Two:  He spent 1/3 of his remaining allowance, which was (2/5)A. 
So on day two, John spent (1/3)(2/5)A.

So how much does he have left? At the beginning of day 2, he had (2/5)A. Then he spent (1/3)(2/5)A. Exactly like we did in day 1, we can count how much he has left by subtraction:

(2/5)A - (1/3)(2/5)A = (2/3)(2/5)A

If this is hard to understand immediately, then replace (2/5)A with x...

x - (1/3)x = (2/3)x

...then look again at our previous calculation.

So after the toy store, John has (2/3)(2/5)A.

Finally:  Then John spent all his money, $0.80, at the candy store. 
That means (2/3)(2/5)A = .80

Now we can do the math and solve for A.

(2/3)(2/5)A = .80
(4/15)A = .80
4A = 12.00
A = 3.00

SherLocked2018 · Answer

Let total be x. 
John spent on day 1 : 3x/5. Rem 2x/5. 
Amt spent Next day: 2x/15. 
Lastly he spent remaining 0.8. 
Thus : 3x/5 + 2x/15 + .8 = x Solving for x we get x = 3.

Alternately, we can plug in options. 
I always start by plugging in B, since the options are in increasing order. so let total be 3. 
Day 1 : 3*3/5 = 1.8 spent. Rem 1.2. 
Day 2 : 1.2/3 = .4 spent. Rem .8. 
Correct. 
Ans B.

OptimusPrepJanielle · Answer

Let his allowance be x. Amount spent at arcade = 3x/5 Remaining = 2x/5 Amount spent at toy store = 1/3(2x/5) Last amount remaining = $0.80 Hence 3x/5 + 1/3(2x/5) + 0.80 = x So, x = 3 Hence option (B). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

JeffTargetTestPrep · Answer

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

Jordi12345 · Answer

Counting backwards here;

0.8 = 66.6% so, total before that is 1.2 dollars

1.2 dollars is 2/5, so 1/5 is 0.6 dollars of total

5 times 0.6 dollars = 3 dollars in total

Abhishek009 · Answer

Let the weekly allowance be 15 (LCM of 5 & 3 )

Amount spent on day 1 = 9 ; Amount left = 6
Amount spent on day 2 = 2 ; Amount left = 4

Now, 4 represents $0.80.
So, 1 represents $0.20
And , 15 represents $ 3.00 , Answer must be (B)

Kimberly77 · Answer

Hi  BrentGMATPrepNow , is calculating as below correct also and can you see any issue with it? Thanks Brent.
3/5 x - 1/3 x = 0.8
4x/15 = 0.8
x=3

BrentGMATPrepNow · Answer

Those calculations are correct (I'll add one extra line for absolute clarity):
(3/5)x - (1/3)x = 0.8
(9/15)x - (5/15)x = 0.8
(4/15)x = 0.8
x=3

Kimberly77 · Answer

Brilliant thanks  BrentGMATPrepNow  for confirmaiton.

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

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