Chapter 6.1, Problem 55MR

To determine

To solve the equation $\frac{1}{2}x+\frac{1}{3}y=5$ for $y$ .

Answer to Problem 55MR

  $y=\frac{3}{2}\left(10-x\right)$

Explanation of Solution

Given:

  $\frac{1}{2}x+\frac{1}{3}y=5$

Calculation:

  $\begin{array}{l}\frac{1}{2}x+\frac{1}{3}y=5\\ \Rightarrow \frac{3x+2y}{6}=5\\ \Rightarrow 3x+2y=30\\ \Rightarrow 2y=30-3x\\ \Rightarrow 2y=3\left(10-x\right)\\ \Rightarrow y=\frac{3}{2}\left(10-x\right)\end{array}$