Chapter 4.5, Problem 40PPS

To determine

To solve and check: the given equation

Answer to Problem 40PPS

The required solution is $x=240$

Explanation of Solution

Given: $\frac{x}{2}+\frac{5x}{6}+\frac{x}{4}=380$

Calculation:

To solve equation and check the solution

  $\frac{x}{2}+\frac{5x}{6}+\frac{x}{4}=380$

LCD is 12. Make the right side of equation to have denominator 12

  $\begin{array}{l}\frac{1\cdot 6}{2\cdot 6}x+\frac{5\cdot 2}{6\cdot 2}x+\frac{1\cdot 3}{4\cdot 3}x=380\\ \frac{6}{12}x+\frac{10}{12}x+\frac{3}{12}x=380\\ \frac{6+10+3}{12}x=380\end{array}$

Multiply both sides of equation with $\frac{12}{19}$

  $\begin{array}{l}x=380\cdot \frac{12}{19}\\ x=240\end{array}$

Solution:- $x=240$

Check

Substitute $x=240$ in $\frac{x}{2}+\frac{5x}{6}+\frac{x}{4}=380$

  $\begin{array}{l}\frac{240}{2}+\frac{5\left(240\right)}{6}+\frac{240}{4}=380\\ 120+200+60=380\\ 380=380\end{array}$

Hence verified. So solution is $x=240$

Conclusion:

Therefore, the required solution is $x=240$