Question

$\frac{1}{2}$ is subtracted from a number and the difference is multiplied by $4$. If $25$ is added to the product and the sum is divided by $3$, the result is equal to $10$. Find the number

• A. $\frac{3}{5}$
• B. $\frac{7}{4}$
• C. $\frac{6}{7}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{7}{4}$

Let the number be $x$

When subtracted $\frac{1}{2}$ we get

$x-\frac{1}{2}$

Multiply by $4,$ we get

$(x-\frac{1}{2})\times 4$

Adding $25$, we get

$4(x-\frac{1}{2})+25$

Dividing by $3,$ we get

$(4(x-\frac{1}{2})+25)÷3$

Given that the number is equal to $10$

$\therefore [4(x-\frac{1}{2})+25]÷3=10$

Multiply both sides by $3,$ we get

$[4(x-\frac{1}{2})+25]÷3\times 3=10\times 3$

$\Rightarrow 4(x-\frac{1}{2})+25=30$

$\Rightarrow 4x-2+25=30$

$\Rightarrow 4x=30-25+2$

$\Rightarrow 4x=7$

$\Rightarrow x=\frac{7}{4}$