Question

the sum of the digits of a two-digit counting number is 14. The product of the digits is 20 less than the number. What is the number?

Answer 1

68

Explanation:

Let the 2 digit no. be

x tens and y units

= 10x + y

x + y = 14 (1)

x × y = (10x + y) - 20

xy = 10x + y - 20

xy - 10x - y = -20

x(y-10) - y = -20 (2)

(1) x = 14 - y

(2) (14-y)(y-10) - y = -20

14y - 140 - y² + 10y - y = -20

y² - 23y + 120 = 0

y² - 15y - 8y + 120 = 0

y(y - 15) - 8(y - 15) = p

(y - 15)((y - 8) = 0

y = 15, 8

Since x and y are single digits,

y = 8

x = 14 - y

x = 14 - 8

x = 6

The number is 68