Solve A = P + Prt for t

Step by step

The question

Question: solve for t in A = P + Prt.

We treat the other letters like numbers.

1 t on the left

t is on the right.

We swap the two sides, so t is on the left.

They are still equal.

2 Remove the P

We want t by itself.

The P is in the way.

To remove P, we take away P.

We do it on both sides.

They make zero.

Cross them out.

Now we have Prt = A − P.

3 Remove the Pr

Prt means Pr times t.

We want just t.

To remove times Pr, we divide by Pr.

We do it on both sides.

Pr divided by Pr is 1.

So just t is left.

So t = (A − P) over Pr.

4 Check

Let's check with numbers.

We pick A = 8, P = 2, r = 3.

Our answer gives t = 1.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 8.

So our answer is right!

Let's look back.

First: t on the left.

Then: remove the P.

Then: remove the Pr.

Last: check.