Question

The sum of 5/6 and twice a number is equal to 2/3 subtracted from three times the number. Find the number

Answer 1

SOLUTION

Given the question, the following are the solution steps to answer the question.

STEP 1: Interpret the statement

Let the number be y

From first statement,

$\begin{gathered} twice\text{ the number}=2y \\ 2y+\frac{5}{6}=3y-\frac{2}{3} \end{gathered}$

STEP 2: Evaluate the equation to get y

$\begin{gathered} \mathrm{Subtract\:}\frac{5}{6}\mathrm{\:from\:both\:sides} \\ 2y+\frac{5}{6}-\frac{5}{6}=3y-\frac{2}{3}-\frac{5}{6} \\ 2y=3y-\frac{3}{2} \\ \mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides} \\ 2y-3y=3y-\frac{3}{2}-3y \\ -y=-\frac{3}{2} \\ \mathrm{Divide\:both\:sides\:by\:}-1 \\ \frac{-y}{-1}=\frac{-\frac{3}{2}}{-1} \\ y=\frac{3}{2} \end{gathered}$

Hence, the number is 3/2