Chapter 4.7, Problem 6WE

To determine

To solve the equation $A=P+Prt$ , for t .

Answer to Problem 6WE

  $t=\frac{A-P}{Pr},P,r\ne 0$

Explanation of Solution

Given:

The equation, $A=P+Prt$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Calculation:

To solve the given equation $A=P+Prt$ for t , isolate the variable term t on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate t on right side, first subtract P from both sides and then simplify further by dividing $Pr$ from both sides as shown below,

  $\begin{array}{c}A=P+Prt\\ A-P=P+Prt-P\\ A-P=Prt\\ \frac{A-P}{Pr}=\frac{Prt}{Pr}\\ \frac{A-P}{Pr}=t\\ \Rightarrow t=\frac{A-P}{Pr}\end{array}$

Thus, on solving for the indicated variable it gives $t=\frac{A-P}{Pr}$ .

Since it is a rational expression after solving for the indicated variable, so the denominator should not be zero. That is, $P,r\ne 0$ .