Question

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number?

Answer 1

the digit is x and y

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number
7(x+y) = 10x+y
7x+7y = 10x+y
6y = 3x
x = 2y

If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits
10y+x = x+y+18
9y = 18
y = 2
x = 2(2) = 4

so the original number is 42