Question

Sum of two numbers is 81. One is twice the other.

1. If smaller number is x, the other number is ______.
2. The equation formed is ______.
3. The solution of the equation is ______.
4. The numbers are ______ and ______.

Answer 1

1. If smaller number is x, the other number is 2x.
2. The equation formed is x + 2x = 81.
3. The solution of the equation is 27.
4. The numbers are 27 and 54.

Explanation:

a. We are given that one number is twice the other. If smaller number is x, then the other number is 2x.

b. We are given that sum of two numbers is 81. So, the equation will be x + 2x = 81.

c. Now, solve the equation for x,

⇒ x + 2x = 81

⇒ 3x = 81

⇒ `(3x)/3 = 81/3`  ...[Dividing both sides by 3]

x = 27

Hence, the solution of the equation is 27.

d. The two numbers are x = 27 and 2x = 2 × 27 = 54.