Question

When Raju multiplies a certain number by 17 and adds 40 to the product, he gets 225. Find the number.

Answer 1

Hint: We assume the number Raju multiplies by 17 as $x.$ The product of the unknown number and 17 is $17x.$Raju adds 40 to the product and gets the number 225 which we write $17x+40=225.$ We solve the linear equation in 1 variable to get $x.$

Complete step-by-step solution
We know that the general linear equation of one variable is given by \[ax=b\]
Here $x$ is the unknown variable, $a$ and $b$ are known real numbers also called constants and $a$ cannot be zero. We also know that if we add, subtract, divide or multiply the same number on both sides of the equation then the equality condition will still hold.\[\]
We are given the question that the number with which Raju is multiplying is ‘certain’ which means it can only take a single value at one time. Let us assume that number as $x$. We are given the question that Raju multiplies the unknown number with 17. We can write the product of the unknown number and 17 in terms of $x$ as,
\[x\times 17=17\times x=17x\]
It is also given that he adds 40 to the product. We can write the sum of the product and 40 as
\[17x+40\]
Raju gets the number 225 after addition. So the sum is equal to 225. We have,
\[17x+40=225...\left( 1 \right)\]
The above equation is a linear equation in one variable. We have to solve it to get the unknown number $x$ as required in the question. We subtract 40 on both sides of the equation (1) and have,
\[\begin{align}
  & 17x+40-40=225-40 \\
 & \Rightarrow 17x=185 \\
\end{align}\]
We divide both side of the equation by 17 and have,
\[\begin{align}
  & \Rightarrow \dfrac{17x}{17}=\dfrac{185}{17} \\
 & \Rightarrow x=\dfrac{185}{17} \\
\end{align}\]
So the unknown number is a fraction $\dfrac{185}{17}$.

Note: We note that we can divide both sides of the linear equation by only a nonzero number. We can also take the same exponent on both sides of the equation. We need at least one linear equation for one variable, two equations for two variables which is given by ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$ and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$where ${{a}_{1}},{{a}_{2}},{{b}_{1}},{{b}_{2}},{{c}_{1}},{{c}_{2}}$ are real numbers.