Question

A two digit number is seven times the sum of its digits and also equal to 12 less than three times the product of its digits. Find the numbers.

Answer 1

Let the tens digit be x and the units digit be y.

Form the number

Number = 10x + y

(i) Number is seven times the sum of its digits

10x + y = 7(x + y)

10x + y = 7x + 7y

3x = 6y

x = 2y     ...(1)

(ii) Number is 12 less than three times the product of its digits

10x + y = 3(xy) − 12     ...(2)

Substitute x = 2y in equation (2)

10(2y) + y = 3(2y ⋅ y) − 12

21y = 6y² − 12

6y² − 21y − 12 = 0

Divide by 3:

2y² − 7y − 4 = 0

(2y + 1) (y − 4) = 0

y = 4 or y = `-1/2`

x = 2y = 8

The required two-digit number is: 84