Expert: Sherry Wallin - 6/1/2010

Question
I need to find out why and how of a
math problem (seemingly basic) that I just
can't figure out on my own, and may be hard
for me to explain, it involving
percentages, hope you understand, thanks!
It may be kind of stupid, dumb, or useless,
but I just wanted to know if there is some
kind of equation for it.

let's say we're exchanging currencies for our scenario.

let's also say the euro is pegged at 1.30 for every 1.00 dollar.

so when we exchange these currencies, since the euro is 30%
more than the dollar (in quantity), the person would add 30% to how ever many dollars the person was exchanging (right?) to figure how many euros they would give back.

so now, we're exchanging 1,000 dollars into euros, I would
get back 1,300 euros (eh?). Let's now say I wanted to
immediately reverse the transaction. Now I run into a problem
I can't use the 30% amount any more for reversal (because it's a higher amount now) 1,300 euros minus 30% is 910, and not 1,000.

my questions (finally, I know) is what kind of equation can be used for an equal reversal back to the same amount, using the same percentage amount. Do I have to take less away from the percentage (on the conversion back) for every certain amount that is added on or something? Sorry, this may be ridiculous, hope you can enlighten me, if it makes sense. If not, just disregard. Thanks.

Answer
Mike~
    When you change from  dollars to euros and the rate is 1.3 euros for each dollar you are just using the ratio of 130/100 = 1.3/1 or even 13/10. So you want to change 53 dollars into euros so simply multiply: 10 dollars/13 euros * 52 euros = 10 dollars *4 (since 52 euros/**13 euros is 4). Notice you wanted dollars so you used the conversion rate as dollars/euros so that the euros canceled out (numerator to denominator cancel). So suppose you want to convert dollars to euros so use the conversion rate as euros/dollars then you have 70 dollars * 13 euros/10 dollars and now the dollars cancel out leaving you with:
7*13 euros = 91 euros. If this is not clear or you want further explanation please feel free to send more questions.

Math Prof

**There was a typo, instead of 52 euros/4 euros it should have been 52 euros/13 euros = 4, sorry :(