Question

The sum of two digits is 8. If 72 is subtracted from the number, the number is equal to the tens digit in the number. Find the number

Answer 1

Answer:

Let a and b represent the two digits of the number.

From the question we know the following:

a + b = 10

(10a + b) - 72 = (10b + a)

The second equation can be rearranged as follows:

9a - 9b = 72

a - b = 8

We now have:

a + b = 10

a - b = 8

We can add these two equations together to get:

2a = 18

a = 9

Plugging that answer into second equation:

9 - b = 8

b = 1

So our original number is 91.

Here is another way to solve it. There are only three two-digit numbers larger than 72 whose digits add up to 10: 73, 82, and 91.

73 - 72 = 1

82 - 72 = 10

91 - 72 = 19

So our answer (again) is 91.