The units' digit of a two-digit number is 7 more than the tens' digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.

Let the digit in the tens place be x

tens place = x (therefore the value is 10x)

ones place = x + 7

The number is 10x + x + 7

Add 26 to it

10x + x + 7 + 26 = 11x + 33

It is 5 times the sum of the digit

11x + 33 = 5 (x + x + 7)

11x 33 = 10x + 35

x = 2

x + 7 = 2 + 7 = 9

So the number is 29