# Thread: Transposing a fraction with the same unknown

1. ## Transposing a fraction with the same unknown

I am struggling to transpose my OWN formula, my math skills are terrible. I have:
$\displaystyle 1.5=(x+10)/(x+5)$

I know x is 5 because I made this problem. How do I reverse it and make x the subject?

I've been trying to work with the PIN example which generally makes sense:
P=I/N
I=P*N
N=N*I is this right?

What is the best way to remember this? How do you think about this in your head? Why are percentages so easy but this seems to confuse the hell out of me?

Sam

2. Hello Unmath Sam
Originally Posted by Unmath Sam
I am struggling to transpose my OWN formula, my math skills are terrible. I have:
$\displaystyle 1.5=(x+10)/(x+5)$

I know x is 5 because I made this problem. How do I reverse it and make x the subject?

I've been trying to work with the PIN example which generally makes sense:
P=I/N
I=P*N
N=N*I is this right?

What is the best way to remember this? How do you think about this in your head? Why are percentages so easy but this seems to confuse the hell out of me?

Sam
You want to solve the equation
$\displaystyle 1.5=\frac{x+10}{x+5}$
First, get rid of fractions, by multiplying both sides of the equation by $\displaystyle (x+5)$:
$\displaystyle \Rightarrow 1.5(x+5) = x+10$
Next, remove brackets:
$\displaystyle \Rightarrow 1.5x+7.5=x+10$
Collect $\displaystyle x$'s on one side; everything else on the other:
$\displaystyle \Rightarrow 1.5x-x=10-7.5$
Simplify:
$\displaystyle \Rightarrow 0.5x = 2.5$
Divide to complete the solution:
$\displaystyle \Rightarrow x = \frac{2.5}{0.5}=5$
As far as your other questions are concerned, I'll just correct one of your equations:
$\displaystyle P = \frac{I}{N}$

$\displaystyle \Rightarrow I=PN$ (You got this line correct)

$\displaystyle \Rightarrow N = \frac{I}{P}$ (I think this is what you meant here)

3. ## Slightly different approach

Here's a slightly different approach.

$\displaystyle 1.5 = \tfrac{3}{2}$

$\displaystyle \frac{3}{2} = \frac{x+10}{x+5}$

Multiplying both sides by (x+5):

$\displaystyle \frac{3x+15}{2} = x+10$

$\displaystyle \frac{3x+15}{2}-x = 10$

$\displaystyle \frac{3x+15-2x}{2} = 10$

$\displaystyle \frac{x+15}{2} = 10$

$\displaystyle x+15 = 20$

$\displaystyle x = 5$

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