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

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 - [ (1/3)A + (2/15)A ]= A - (11/15)A = (4/15)A

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

A = $3.00

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

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

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

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

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

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

Answer is B

Let Allowance be x

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

X= 3

Ans B

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

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.

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).

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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

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

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)

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

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

Brilliant thanks BrentGMATPrepNow for confirmaiton.