Question

The sum of two numbers is 60 and their difference is 30.

1. If smaller number is x, the other number is ______. (use sum)
2. The difference of numbers in term of x is ______.
3. The equation formed is ______.
4. The solution of the equation is ______.
5. The numbers are ______ and ______.

Answer 1

1. If smaller number is x, the other number is 60 – x. (use sum)
2. The difference of numbers in term of x is 60 – 2x.
3. The equation formed is 2x = 30.
4. The solution of the equation is 15.
5. The numbers are 15 and 45.

Explanation:

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. Given, one number = x  ...[From (a)]

Then, other number = (60 – x)

∴ Difference = (60 – x) – x = 60 – 2x

c. We are given that difference between two numbers is 30

So, the equation formed is 60 – 2x = 30

⇒ –2x = 30 – 60   ...[Transposing 60 to RHS]

⇒ –2x = –30

⇒ 2x = 30  ...[Multiplying both sides by (–1)]

d. Let us solve the equation for x,

2x = 30

On dividing the above equation by 2, we get

`(2x)/2 = 30/2`

⇒ 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