Question

How would i simplify this?
The equation is I/Pr=I/Pr.
105/P(.07)=80/(P+100)(.05)

Answer 1

That is very, very difficult to translate.

Your equation is senseless \(\dfrac{I}{Pr} = \dfrac{I}{Pr}\). Obviously, something is equal to itself. That is neither interesting nor useful.

What you seem to want to know is the amount of two investments that will give specific returns over the same period of time. This would mean that there are two different I's, two different P's, and two different r's.

In your working, so far, you have used the symbol "P" to mean THREE different things!

Very confusing. Try really hard to write things that make sense on paper. I'm sure this all made sense in your head, but it didn't when you wrote it down.

Sometimes, it helps to use subscripts. Sometimes, just use different variables. The world will not come to and end if you use "B" to mean some other investment - different from P.

Next, you have not quite remembered your Order of Operations.

105/P(.07)=80/(P+100)(.05)

This means: \(\dfrac{105}{P}\cdot (0.07) = \dfrac{80}{P+100}\cdot (0.05)\)

I believe this is not what you meant,

Had you written this: 105/[P(.07)]=80/[(P+100)(.05)]

It would have read as you intended. \(\dfrac{105}{P(0.07)} = \dfrac{80}{(P+100)(0.05)}\)

Well, this is where I need more information from you. Is the last equation correct? We have two investments, one $100 more than the other. Given the same length of time, one earns $105 @ 7% and the other earns $80 at 5%.

Am I close?