Question

Question 19

The sum of the 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

Given the sum of two numbers is 60 and difference is 30.
(a) If the smaller number is x, then the other number is (60 - x), since the sum of both numbers is 60.

(b) Let one number = x
Then, the other number = (60 - x)
$\therefore$ (60 - x) - x = 60 - 2x

(c) We are given that difference between two numbers is 30.
So, the equation formed is 60 - 2x = 30
$\Rightarrow -2x=30-60\Rightarrow -2x=-30\Rightarrow 2x=30$

(d) Let us solve the equation for x,
2x = 30
On dividing the above equation by 2, we get
$\frac{2x}{2}=\frac{30}{2}\Rightarrow x=15$
Hence, the solution of the equation is 15.

(e) The numbers are x and (60 - x).
Now, put the value of x, we get
First number = 15
Second number = 60 - 15 = 45