Chapter 4.5, Problem 39PPS

To determine

To solve and check: the given equation

Answer to Problem 39PPS

The required solution is $y=15.1$

Explanation of Solution

Given: $40.77=\frac{y}{5}+2.4y+\frac{y}{10}$

Calculation:

To solve equation and check the solution

  $\begin{array}{l}40.77=\frac{y}{5}+2.4y+\frac{y}{10}\\ 40.77=\frac{y}{5}+\frac{24}{10}y+\frac{y}{10}\end{array}$

LCD is 10. Make the right side of equation to have denominator 10

  $\begin{array}{l}40.77=\frac{1\cdot 2}{5\cdot 2}+\frac{24}{10}y+\frac{1}{10}y\\ 40.77=\frac{2+24+1}{10}y\\ 40.77=\frac{27}{10}y\end{array}$

Multiply both sides of equation with $\frac{10}{27}$

  $\begin{array}{l}\frac{40.77\cdot 10}{27}=y\\ y=15.1\end{array}$

Solution:- $y=15.1$

Check

Substitute $y=15.1$ in $40.77=\frac{y}{5}+2.4y+\frac{y}{10}$

  $\begin{array}{l}40.77=\frac{15.1}{5}+2.4\left(15.1\right)+\frac{15.1}{10}\\ 40.77=3.02+36.24+1.51\\ 40.77=40.77\end{array}$

Hence verified. So solution is $y=15.1$

Conclusion:

Therefore, the required solution is $y=15.1$