Percentages and Multiplying Factors

Hello gallon

Quote:

Originally Posted by

**gallon** hi i'm not exactly sure how to put this so please bear with me.

i would like to know how to write this into a calculation.

let's say i owe my friend 11.47. But i have to transfer the money to her and the system takes 4.9% interest.

how much should i send my friend in order to end up with 11.47? how would i put that into an equation?

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**.

For instance, let's suppose we want to make the number $\displaystyle 11.47$ bigger in the ratio $\displaystyle 2:3$. The multiplying factor you'd use to do this is $\displaystyle \frac{3}{2}$; in other words, you'd multiply $\displaystyle 11.47$ by $\displaystyle \frac{3}{2}$. This would make $\displaystyle 11.47$ one-and-a-half times bigger, which is what increasing in the ratio $\displaystyle 2:3$ means.

On the other hand, if you want to make something smaller using this ratio, then the multiplying factor would be $\displaystyle \frac{2}{3}$. And the answer would be $\displaystyle \frac{2}{3}$ 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 $\displaystyle \frac{3}{2}$ will make it bigger; multiplying it by $\displaystyle \frac{2}{3}$ 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 $\displaystyle \frac{100}{95.1}$.

Answer: you send $\displaystyle \frac{100}{95.1}\times 11.47$.

Once you've got hold of it, this method is dead easy!

Grandad