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On a vacation, Rose exchanged $500.00 for euros at an exchange rate of

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On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 14 Jun 2016, 13:38
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On a vacation, Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent \(\frac{3}{4}\) of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 14 Jun 2016, 17:15
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AbdurRakib wrote:
On a vacation,Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent \(\frac{3}{4}\) of the euros she received.If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

Dear AbdurRakib,
This is a great question! Thanks for posting it! I'm happy to respond. :-)

Step #1
She exchanges $500 for euros at 0.8 euro/dollar. Set up a proportion, where x is the number of euros she originally received

(x/$500) = (0.8 euro)/($1)

Cross-multiply and use the doubling & halving rule:
x = 0.8*500 = 0.4*1000 = 400 euros

Step #2
She spends 3/4, so after her wild days in Europe, she is left with just 100 euros.

Step #3
She exchanges 100 euros back to dollars at $1.20 per euro. Again set up a proportion, where y is the number of dollars she gets back.

y/100 = $1.20/(1 euro)

Cross-multiply:

y = $1.20*100 = $120

Answer = (D)

Does all this make sense?
Mike :-)
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 22 Jun 2017, 04:23
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AbdurRakib wrote:
On a vacation,Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent \(\frac{3}{4}\) of the euros she received.If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

No Need to convert $ to Euro and Vice-versa.

Exchange rate of $ to Euro = 0.80
Exchange rate of Euro to $ = 1.20

% of Money Received if she exchanges $500 to Euro and back = 0.8 * 1.2 = 0.96 = 96%

Therefore, there is a 4% Net loss of Money due to exchange.

$ left after Expenditure = \(500*\frac{1}{4} = $125\)
Loss due to Exchange = 4% of 125 = \(\frac{(125*4)}{100}= $5\)

Net $ she is left with = 125 - 5 = $120
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 15 Jun 2016, 00:44
Rose got 400 Euros
She spent 300 Euros
Remaining Euros = 100 Euros
She got $120 (@ $1.20 per euro)
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 02 Dec 2016, 06:47
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AbdurRakib wrote:
On a vacation,Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent \(\frac{3}{4}\) of the euros she received.If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00


We are given that Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar. Since 1 dollar = 0.8 euros, 500 dollars = 500 x 0.8 = 400 euros.

Since she spent spent 3/4 of her euros, she was left with 1/4 x 400 = 100 euros.

Finally, she exchanged her remaining euros for dollars at a rate of 1.20 dollars per euro.

Since 1 euro = 1.20 dollars, she ended up with 100 x 1.2 = 120 dollars.

Answer: D
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 15 Nov 2017, 21:24
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Let me try to help in a simple manner.

$500*0.8*1/4*1.2
= $500*4/5*1/4*6/5
= $120

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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 16 Sep 2018, 14:45
On a vacation, Rose exchanged $500.00 for euros at an exchange rate of 0.80 euro per dollar and spent 3/4 of the euros she received. If she exchanged the remaining euros for dollars at an exchange rate of $1.20 per euro, what was the dollar amount she received?

A) $60.00
B) $80.00
C) $100.00
D) $120.00
E) $140.00

Since nations have their own unique currencies, the need to change from one currency to another is important when one travels from one country to another. This question is based on this scenario.

Step 1: The amount of dollars Rose exchanged originally into euros = $500.00 at the rate of 0.80 euro per dollar.

Step 2: At the rate of 0.8 euro per dollar, $500.00 = 500 x 0.8 = 400 euros. This means that Rose collected 400 euros for the $500 exchanged.

Step 3: Since Rose spent ¾ of the 400 euros she received; the amount she spent is given as: ¾ x 400 = 300 euros. The remaining number of euros that Rose has after spending 300 euros is 400 -300 = 100 euros.

Step4: Rose exchanged the 100 euros that remained back to dollars at an exchange rate of $1.20 per euro. The dollar amount Rose received from this transaction is calculated as follows: 100 x $1.20

Therefore, Rose received .
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 09 Oct 2018, 08:00
i got it correct but in 2.28 min coz i confused the starting point to be 500 euros and then converted the 'spent' amount in euros finally instead of dollars!
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 05 Dec 2018, 10:54
Like many others I solved this the same way. What I did however was to change the decimals to fractions. So 500$ x 4/5 = 400. Then she spent 3/4 of that so 400 x 3/4 = 300. (Or to save time she saved 1/4 of that leading to 100). Then she exchanged 100 euros back to dollars at 1.2. Thus 100 x 1.2 = 120.

500$ x 4/5 = 400 euros total
400 euros x 1/4 remaining = 100 euros remaining
100 euros x 1.2 exchange rate = 120$

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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 15 Apr 2019, 20:05
There's a speedy method here, provided that you've memorized your fractions:
Recognize that 0.8 euros can be stated as the fraction 4/5... then you are left with the much faster equation of (500 dollars)*(4/5 euros)=400 euros

If she spends 3/4th of what she has: (400 euros)(3/4)=300 euros. She has 100 euros remaining. Just convert that to dollars:
(100 euros)(1.20 dollars/1 euro)=120 dollars.
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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of  [#permalink]

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New post 11 May 2019, 05:01
Sample☺

Dollar to euro rate is .8
500*.8=400 euro
Spent =3/4*400=300
Remaining euro =400-300=100
So, converted to dollar =100*1.2=120 dollar

Answer:D

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Re: On a vacation, Rose exchanged $500.00 for euros at an exchange rate of   [#permalink] 11 May 2019, 05:01
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