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

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+(5)/(6)=3y-(2)/(3) \end{gathered}`

STEP 2: Evaluate the equation to get y

`\begin{gathered} \mathrm{Subtract\:}(5)/(6)\mathrm{\:from\:both\:sides} \\ 2y+(5)/(6)-(5)/(6)=3y-(2)/(3)-(5)/(6) \\ 2y=3y-(3)/(2) \\ \mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides} \\ 2y-3y=3y-(3)/(2)-3y \\ -y=-(3)/(2) \\ \mathrm{Divide\:both\:sides\:by\:}-1 \\ (-y)/(-1)=(-(3)/(2))/(-1) \\ y=(3)/(2) \end{gathered}`

Hence, the number is 3/2