The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number? Can I get an example of this math problem in a real world scenario?

Answer 1

T is the tens digit

O is the ones digit

T + O = 7.

The original number is 10T + O

The reverse digits is 10O + T

Reversing the digits increases the number by 9

10O + T = 10T + O + 9

10O + T - 10T - O = 9

9O - 9T = 9

9(O - T) = 9

O - T = 1

So

O + T = 7

O - T = 1

Adding them together

2O = 8

O = 4

The ones digit is 4, so the tens digit must be 3, since T = 7-O = 7-3 = 4

So the original number is 34.

Note that 43 - 34 = 9

You can also figure it out by process of elimination using the following table,

as the digits must add up to 7.

Original number reverse digits difference

16 61 45

25 52 27

34 43 9 <--- there it is