Question

How do you solve `A = P + Prt` for `t`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Subtract `color(red)(P)` from each side of the equation to isolate the `r` term while keeping the equation balanced:

`A - color(red)(P) = -color(red)(P) + P + Prt`

`A - P = 0 + Prt`

`A - P = Prt`

Now, divide each side of the equation by `color(red)(P)color(blue)(t)` to solve for `r` while keeping the equation balanced:

`(A - P)/(color(red)(P)color(blue)(t)) = (Prt)/(color(red)(P)color(blue)(t))`

`(A - P)/(Pt) = (color(red)(cancel(color(black)(P)))rcolor(blue)(cancel(color(black)(t))))/(cancel(color(red)(P))cancel(color(blue)(t)))`

`(A - P)/(Pt) = r`

`r = (A - P)/(Pt)`

Or

`r = A/(Pt) - P/(Pt)`

`r = A/(Pt) - color(red)(cancel(color(black)(P)))/(color(red)(cancel(color(black)(P)))t)`

`r = A/(Pt) - 1/t`

Answer 2

`t=(A-P)/(Pr)`

Explanation:

Given:`" "A=P+Prt`

Factor out the `P`

`A=P(1+rt)`

Divide both sides by P

`A/P=1+rt`

Subtract 1 from both sides

`A/P-1=rt`

Divide both sides by r

`A/(Pr)-1/r=t" "->" "t=A/(Pr)-1/r`

Or could write this as:

`t=(A-P)/(Pr)`