Percentages and Multiplying Factors
If you want to solve problems like this without using algebra (and who doesn't!), it's worth trying to understand multiplying factors. These are things you multiply by to make a number bigger or smaller in a particular ratio.
Originally Posted by gallon
For instance, let's suppose we want to make the number bigger in the ratio . The multiplying factor you'd use to do this is ; in other words, you'd multiply by . This would make one-and-a-half times bigger, which is what increasing in the ratio means.
On the other hand, if you want to make something smaller using this ratio, then the multiplying factor would be . And the answer would be of the number you started with.
In other words, to make a number bigger, the bigger number goes on the top of the multiplying factor; to make it smaller, the smaller number goes on the top. Multiplying something by will make it bigger; multiplying it by will make it smaller.
So what about your problem? Well, for every 100 pennies you send, the system takes 4.9 pennies, so your friend gets what's left: 95.1 pennies. The key numbers in this problem are the number of pennies you send and the number your friend receives; in other words 100 and 95.1. Now you've obviously got to send more than 11.47, so we need to make 11.47 bigger. This tells us to use a multiplying factor of .
Answer: you send .
Once you've got hold of it, this method is dead easy!