SOLUTION: The value of 100 Euros in Different Currencie are: US Dollar 133.8 British Pounds 89.9 Australian Dollars 143.2 Russian Ruble 4239.6 Que

Question 1164649: The value of 100 Euros in Different Currencie are:
US Dollar 133.8
British Pounds 89.9
Australian Dollars 143.2
Russian Ruble 4239.6
Questions:
1) 45 British pounds is approximately to how many russian ruble?
2) Approximately how many Euros will you get for 100 Australian Dollars?
3) Approximately how many US Dollars will you get for 48 Australian Dollars?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
100 euros is equivalent to:
133.8 us dollars
89.9 british pounds
143.2 australian dollars
4239.6 russian rubles

they're all equal to 100 euros, so we can compare them directly by eliminating the middle man.

for example:
let e = 100 euros
let r = equivalent number of russian rubles
let u = equivalent number of us dollars

ratio of u to e is equal to u/e.
ratio of r to e is equal to r/e.
ratio of u to r is equal to (u/e)/(r/e) which is equal to (u/e) * (e/r) which makes it equal to u/r.
ratio of r to us is equal to (r/e)/(u/e) which is equal to (r/e) * (e/u) which makes it equal to r/u.

with that in mind, we should be able to answer the questions directly without requiring the intervention of the middle man of euros.

the questions are:

1) 45 British pounds is approximately to how many russian ruble?

to answer this question, we need to know the number of russian rubles per british pound.

that ratio would be 4239.6 / 89.9

45 british pound is therefore equivalent to 45 * 4239.6 / 89.9 = 2122.157953 russian rubles.

2) Approximately how many Euros will you get for 100 Australian Dollars?

100 euros is equivalent to 143.2 australian dollars.

to answer this question, we need to know the number of euros per australian dollar.

that ratio would be 100 / 143.2

100 australian dollars is therefore equivalent to 100 * 100 / 143.2 = 69.83240223 euros.

3) Approximately how many US Dollars will you get for 48 Australian Dollars?

to answer this question, we need to know the number of us dollars per australian dollar.

that ratio would be 133.8 / 143.2.

48 australian dollars is therefore equivalent to 48 * 133.8 / 143.2 = 44.87916201 us dollars.

note that these are not the current exchange rates.

the current exchange rates for 100 euros is:
us dollar 117.881
british pound 90.8688
australian dollar 162.609
russian ruble 8933.13

i used the current exchange rates to confirm the arithmetic was sound.

for example, 45 british pounds to russian rubles would be 45 * 8933.13 / 90.8688 = 4423.86 russian rubles.
i used the exchange converter for british pounds to russian rubles directly to confirm this was accurate.
it was.

note that the middle man was 100 euros and they canceled out in the arithmetic.

for example, using the current exchange rate:

ratio of russian rubles to euros is 8933.13 / 100
ratio of british pounds to euros is is 90.8688

ratio of russian rubles to british pounds is (8933.13/100) / (90.8688/100) which becomes 8933.13/100 * 100/90.8688 which then becomes 8933.13/90.8688 because the 100 in the numerator and denominator cancels out.
8933.13/90.8688 * 45 = 4423.86 - same as i got earlier.

note again, this was using the current exchange rate.
the problem exchange rate was used to provide your solutions.

they are, once again.

45 british pound is equivalent to 45 * 4239.6 / 89.9 = 2122.157953 russian rubles.

100 australian dollars is equivalent to 100 * 100 / 143.2 = 69.83240223 euros.

48 australian dollars is equivalent to 48 * 133.8 / 143.2 = 44.87916201 us dollars.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The response from the other tutor is exceedingly long and wordy, making it hard to follow.

In the last few lines of that response, he gets to the basic process of converting units.

To change units without changing a measurement, multiply by a "unit fraction" in which the numerator and denominator are equal measurements but in different units.

For a simple example....
12 inches 4*12 4 feet * --------- = ---- = 48 inches 1 foot 1

The units "cancel" resulting in a measurement in different units.

In this problem, you are given the value of 100 Euros in several currencies. So the ratio of any two of those numbers is a unit fraction.

(1) 45 pounds in rubles: multiply by rubles/pounds
4239 rubles 45 pounds * ------------ 89.9 pounds

(2) 100 Australia dollars in Euros: multiply by Euros/Australia dollars
100 Euros 100 Australian dollars * ------------------------ 143.2 Australian dollars

(3) 48 Australian dollars in US dollars: multiply by US dollars/Australian dollars
133.8 US dollars 48 Australian dollars * ------------------------ 143.2 Australian dollars

You can do the calculations.

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