Q7. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

The sum of one fifth of a number and three is equal to half of the number. What is the number?

A $5$                             C $\mathbf{15}$

B $\mathbf{10}$                           D $\mathbf{20}$

Step-by-Step Solution

Answer

The number is 10.

Step 1. Given information.

The sum of one fifth of a number and three is equal to half of the number.

Step 2. Concept used.

Translate the sentence into the equation.

So, suppose the number is a.

The equation is:

$\begin{array}{l}\frac{1}{5}a+3=\frac{1}{2}a\\ \Rightarrow \frac{1}{5}a-\frac{1}{2}a=-3\\ \Rightarrow -\frac{3}{10}a=-3\\ \Rightarrow \frac{3}{10}a=3\\ \Rightarrow a=10\end{array}$ 

Step 3. To find the value of a.

$\begin{array}{l}\frac{1}{5}a+3=\frac{1}{2}a\\ \Rightarrow \frac{1}{5}a-\frac{1}{2}a=-3\\ \Rightarrow -\frac{3}{10}a=-3\\ \Rightarrow \frac{3}{10}a=3\\ \Rightarrow a=10\end{array}$

Therefore, the number is 10.

Hence, the correct option is B.