Question

a+3=$\left( 2a+7 \right)\div r$ . How do you make $a$ the subject of the formula?

Answer 1

Hint: Here in this question we have been asked to find the formula for $a$ in terms of $r$ using the given arithmetic expression $a+3=\left( 2a+7 \right)\div r$ . For answering this question, we will perform simple basic arithmetic operations like transforming and multiplication.

Complete step by step solution:
Now considering from the question we have been asked to find the formula for $a$ in terms of $r$ using the given arithmetic expression $a+3=\left( 2a+7 \right)\div r$ .
For answering this question, we will perform simple basic arithmetic operations like transforming and multiplication.
Firstly we will transfer $a+3$ from left hand side to right hand side then $r$ from right hand side to left hand side. After doing that we will have
 $\begin{align}
  & \Rightarrow a+3=\dfrac{2a+7}{r} \\
 & \Rightarrow 1=\dfrac{2a+7}{r\left( a+3 \right)} \\
 & \Rightarrow r=\dfrac{2a+7}{a+3} \\
\end{align}$ .
Now we will further simplify the expression and write it as
\[\begin{align}
  & \Rightarrow r=\dfrac{2a+6+1}{a+3} \\
  & \Rightarrow r=\dfrac{2(a+3)+1}{a+3} \\
 & \Rightarrow r=2+\dfrac{1}{a+3} \\
\end{align}\] .
Now we will transfer $2$ from right hand side to left hand side. After that we will have $ r-2=\dfrac{1}{a+3}$ .
By further simplifying this we will have $\Rightarrow a+3=\dfrac{1}{r-2}$ .
Now we will transfer $3$ from the left hand side to the right hand side. After that we will have $\Rightarrow a=\dfrac{1}{r-2}-3$ .
By further simplifying this we will have
$\begin{align}
  & \Rightarrow a=\dfrac{1-3r+6}{r-2} \\
 & \Rightarrow a=\dfrac{7-3r}{r-2} \\
\end{align}$
Therefore we can conclude that the formula having $a$ as its subject in terms of $r$ using the given arithmetic expression $a+3=\left( 2a+7 \right)\div r$ will be given as $a=\dfrac{7-3r}{r-2}$ .

Note: While answering questions of this type we should be sure with our concepts that we are going to apply in the process and the calculations that we are going to perform in between the steps. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. Someone can understand the question wrongly and write the formula for expressing $r$ in terms of $a$ then we will have $r=\dfrac{2a+7}{a+3}$ .