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

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

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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
[Reveal] Spoiler: OA

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

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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 [#permalink]

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New post 14 Jun 2016, 23:44
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 [#permalink]

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

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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 [#permalink]

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New post 15 Nov 2017, 20:24
Let me try to help in a simple manner.

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

Posted from my mobile device

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Re: On a vacation,Rose exchanged $500.00 for euros at an exchange rate   [#permalink] 15 Nov 2017, 20:24
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On a vacation,Rose exchanged $500.00 for euros at an exchange rate

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