Question

If $\frac{3+x}{7+x}=\frac{3}{7}+\frac{3}{7}$, then $x=$?

$\begin{array}{l}\text{A}.\frac{3}{7}\text{B.3}\\ \text{C}.\text{7D.21}\end{array}$

Short answer

The value of x is21. Option D is correct.

Step-by-step solution

Step-1 – Apply the concept of addition of fractions

The two fractions are added when their denominator are same. To add the fractions with same denominator, add the numerator of the fractions. When denominators are not same, take the least common multiple and make it same.

Step-2 –Add the fractions

Consider the provided expression.

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

Add the fractions on right hand side of the expression.

Since, the denominator is same so just add the numerator.

$\begin{array}{c}\frac{3+x}{7+x}=\frac{3}{7}+\frac{3}{7}\\ \frac{3+x}{7+x}=\frac{3+3}{7}\\ \frac{3+x}{7+x}=\frac{6}{7}\end{array}$

Step-3 – Simplify the expression

Cross multiply the terms.

Multiply 6 with $7+x$ and 7 with $3+x$.

$\begin{array}{c}7\left(3+x\right)=6\left(7+x\right)\\ 21+7x=42+6x\end{array}$

Rearrange the terms and simply. Combine the like terms.

$\begin{array}{c}7\left(3+x\right)=6\left(7+x\right)\\ 21+7x=42+6x\\ 7x-6x=42-21\\ x=21\end{array}$

Hence, the value of x is 21.