Question

Find the value of x.

$\frac{3x+5}{3}=\frac{18x+5}{7}$

Short answer

The value of x is $\frac{20}{33}$.

Step-by-step solution

Step 1. Given information.

The ratio here given is,

$\frac{3x+5}{3}=\frac{18x+5}{7}$

Step 2. Concept and Formula Used.

The properties of proportion,

if$\frac{a}{b}=\frac{c}{d}$ then,$ad=bc$

The given ratio is$\frac{3x+5}{3}=\frac{18x+5}{7}$,

Step 3. Use the property of proportion, if ab=cd then, ad=bc.

Then,

$\begin{array}{l}7(3x+5)=3(18x+5)\\ 21x+35=54x+15\left(\text{Usingdistributiveproperty}\right)\\ 21x-54x=15-35\\ -33x=-20\end{array}$

Step 4. Divide both sides by -33.

$\begin{array}{l}\frac{-33x}{-33}=\frac{-20}{-33}\\ x=\frac{20}{33}\end{array}$

Therefore, the value of x is$\frac{20}{33}$ .