Question

Find all two digit numbers each of each of which is 7 times the sum of its digits and write with proper mathematical steps how you found them​

Answer 1

Answer:

Number = 84

Step-by-step explanation:

a two digit number is 7 times the sum of its digits and is also equal to 12 less than three times the product of its digit.

Let say number = xy

Value of number = 10x + y

Sum of digit = x + y

10x + y = 7 ( x + y)

=> 3x = 6y

=> x = 2y

Product of digits = xy

Three times the product of digits = 3xy

10x + y  = 3xy - 12

Putting x = 2y

=> 20y + y = 6y² - 12

=> 6y² -21 y - 12 = 0

=> 2y² - 7y - 4 = 0

=> 2y² - 8y + y - 4 = 0

=> 2y(y - 4) + 1(y -4) = 0

=> (2y + 1)(y -4) = 0

=> y = 4

x = 2y = 8

Number = 84