Chapter 3.1, Problem 70SR

To determine

Solve the formula $S=\frac{n}{2}(A+t),\text{for }A$

Answer to Problem 70SR

  $A=\frac{2S}{n}-t$

Explanation of Solution

Given:

The formula $S=\frac{n}{2}(A+t),\text{for }A$

Concept Used:

From the formula $S=\frac{n}{2}(A+t),\text{for }A$ , solve and make the subject as A

Calculation:

Make the subject A from the formula $S=\frac{n}{2}(A+t)$

  $\begin{array}{l}\text{Solve}\text{for}A:\\ S=\frac{n}{2}(A+t)\\ 2·S=2·\frac{n}{2}(A+t)\text{[}\text{Multiply}\text{both}\text{sides}\text{by}2\text{]}\\ 2S=n(A+t)\\ \frac{2S}{n}=\frac{n(A+t)}{n}[\text{Divide}\text{each}\text{side}\text{by}n]\\ \frac{2S}{n}=A+t\\ \frac{2S}{n}-t=A+t-t\text{[}\text{Subtract}t\text{from}\text{both}\text{sides}\text{]}\\ \frac{2S}{n}-t=A\\ A=\frac{2S}{n}-t\end{array}$

Thus, $A=\frac{2S}{n}-t$ from the formula $S=\frac{n}{2}(A+t)$