# Math Help - percentages

1. ## percentages

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?

2. 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?
You are putting a figure $x$ into your friends account, but the bank is taking away 4.9% of that (or, they are taking $0.049x$), but at the end you want your friend to be left with 11.47. The following equation describes this:

$x - 0.049x = 11.47$

$x(1-0.049) = 11.47$

$x = \frac{11.47}{1-0.049}$.

Does that make sense?

3. it worked .

but can you explain how you got to the second step?

4. Originally Posted by gallon
it worked .

but can you explain how you got to the second step?
I just took out a factor of x on the LHS.

$x - 0.049x = x \times 1 - 0.049 \times x = x \times (1-0.049)$

5. oh okay. thank you so much

6. ## Percentages and Multiplying Factors

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

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

$\frac{100}{95.1}\times 11.47$.