Question

John has one third of a dollar, and Sarah gives him one sixth of a dollar $\$x.$ Now John has a total of $\$10.$ Find the value of $x.$

• A. $29$
• B. $58$
• C. $108$
• D. $15$

Answer 1

The correct option is B $58$

Given, the amount of money John has initially $=\$\frac{1}{3}$
Money given to John by Sarah $=\$\frac{x}{6}$
Total money John has $=\$10$
$\therefore \frac{1}{3}+\frac{x}{6}=10$

Step 1: Subtract $\frac{1}{3}$ from both sides of the equation in order to remove $\frac{1}{3}$ on the left hand side.
$\Rightarrow \frac{1}{3}+\frac{x}{6}-\frac{1}{3}=10-\frac{1}{3}\Rightarrow \frac{x}{6}=10-\frac{1}{3}(\because \frac{1}{3}-\frac{1}{3}=0)$
$\Rightarrow \frac{x}{6}=\frac{10\times 3}{1\times 3}-\frac{1}{3}\left(\text{making the denominators equal for}10\text{and}\frac{1}{3}\right)$
$\Rightarrow \frac{x}{6}=\frac{30}{3}-\frac{1}{3}$
$\Rightarrow \frac{x}{6}=\frac{30-1}{3}$
$\Rightarrow \frac{x}{6}=\frac{29}{3}$

Step 1: Multiply both the sides by 6
$\frac{x}{6}\times 6=\frac{29}{3}\times 6$
$\Rightarrow x=\frac{29}{3}\times 2\times 3$
$\Rightarrow x=29\times 2$
$\Rightarrow x=58$

Hence, the value of $x$ is $58.$