Question

The sum of two numbers is $60$ and their difference is $30$.(a) If smaller number is $x$, the other number is _____ (b) The difference of numbers in term of $x$ is _____ (c) The equation formed is ______ (d) The solution of the equation is ______ (e) The numbers are _____ and ______ .

Answer 1

Step 1. The other number is

Let $x$ be the smaller number.

And the sum of two number is $60$

So, the other number is $60–x$.

Step-2 The difference of numbers in term of $x$ is

Now, according to question.

$$\begin{gathered} 60–x-x \\ =60-2x \end{gathered}$$

Step-3 : The equation formed is

$\begin{array}{rcl}60–x–x& =& 30\\ \Rightarrow 60–2x& =& 30\\ \Rightarrow 60–30& =& 2x\\ \Rightarrow 30& =& 2x\\ & \Rightarrow & 2x-30=0\end{array}$

Step-4 The solution of the equation is

$$\begin{gathered} 2x-30=0 \\ \Rightarrow 2x=30 \\ \Rightarrow x=15 \end{gathered}$$

Step-5: finding both the numbers

One number is $x=15$ and

Other number is

$$\begin{gathered} 60-x=60-15 \\ =45 \end{gathered}$$

Hence, the sum of two numbers is $60$ and their difference is $30$.(a) If smaller number is x, the other number is $60-x$.(b) The difference of numbers in term of $x$ is $60-2x$. (c) The equation formed is $2x-30=0$. (d) The solution of the equation is $15$. (e) The numbers are $15$ and $45$.