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

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

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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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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

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Bunuel 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

Kudos for a correct solution.


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

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

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

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New post 24 Mar 2015, 02:46
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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
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]

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Bunuel 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

Kudos for a correct solution.



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

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Bunuel 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

Kudos for a correct solution.


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

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New post 25 Mar 2015, 21:32
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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:
[Reveal] Spoiler:
B


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

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

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

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Let Allowance be x

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

X= 3

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

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New post 30 Mar 2015, 03:29
Bunuel 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

Kudos for a correct solution.


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
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 30 Mar 2015, 10:24
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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.
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Re: Having received his weekly allowance, John spent 3/5 of his allowance [#permalink]

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New post 31 Mar 2015, 03:32
Bunuel 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

Kudos for a correct solution.


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

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Bunuel 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

Kudos for a correct solution.


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

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

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New post 21 Mar 2018, 16:20
Bunuel 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
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Re: Having received his weekly allowance, John spent 3/5 of his allowance   [#permalink] 21 Mar 2018, 16:20
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