A two-digit number is 6 more than the product of 7 and the sum of its digits. The number with the digits reversed is two more than the product of 3 and the sum of its digits. What is the number?

Answer 1

Lets say our two-digit number is X, and its digits are ab

Y will be that number with its digits reversed

"A two digit number is 6 more than the product of 7 and the sum of its digits"

can be represented by

X = 10a + b = 6 + 7(a + b)

Simplifying the right side:

10a -7a = 7b - b + 6

3a = 6b + 6

a = 2b + 2

Therefore 'b' must be less than 4, or 'a' will exceed a single digit. Possible values of (a,b) are then:

(2, 0) (4, 1) (6, 2) (8, 3)

Making the possible values of X:

20 41 62 83

The possible values of reversed number Y:

02 14 26 38

"The number with the digits reversed is two more than the product of 3 and the sum of its digits

Y = 3(a + b) + 2

We can simply test the remaining numbers.

02 is discarded for not being a 2 digit number

14: 3(1 + 4) + 2 = 17

26: 3(2 + 6) + 2 = 26

38: 3(3 + 8) + 2 = 35

Y = 26 is then the reversed two-digit number of the answer

X = 62 is the solution.