Question

The sum of two numbers is $81$. One is twice the other.

(a) If smaller number is $\mathrm{x}$, the other number is _______

(b) The equation formed is _______

(c) The solution of the equation is _______

(d) The numbers are _____ and _____

Answer 1

Given that the sum of two numbers is $81$ and one number is twice the other number.

(a) Find the other number:

If smaller number is $\mathrm{x}$.

Then according to the question, another number is twice of $\mathrm{x}$.

Then the other number $=2\times \mathrm{x}=2\mathrm{x}$

Therefore the other number is $2\mathrm{x}$.

(b) Forming the equation:

Since the sum of these two numbers $=81$

So $\mathrm{x}+2\mathrm{x}=81.........\left(1\right)$

Therefore the equation formed is $\mathrm{x}+2\mathrm{x}=81$.

(c) Solving the equation:

On solving the equation $\left(1\right)$. We get,

$$\begin{gathered} \mathrm{x}+2\mathrm{x}=81 \\ \Rightarrow 3\mathrm{x}=81 \\ \Rightarrow \mathrm{x}=\frac{81}{3} \\ \Rightarrow \mathrm{x}=27 \end{gathered}$$

Therefore the solution to the equation is $27$.

(d) Find the value of numbers:

If $\mathrm{x}=27$

Then $2\mathrm{x}=2\times 27=54$

Therefore the required numbers are $27$ and $54$.