Question

The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

(a) 27
(b) 45
(c) 54
(d) 63

Answer 1

By creating and solving a pair of equations based on the given conditions, we conclude that the two-digit numbers satisfying both conditions are 27 and 45; hence, there are two such numbers.

Step-by-step explanation:

The question asks to find a two-digit number where the sum of this number and the number obtained by reversing its digits equals 66, and the digits of the number differ by 2. Let's represent the tens digit by x and the ones digit by y. So, the number can be expressed as 10x + y and the reversed number as 10y + x.

The first condition can be written as an equation:

• 10x + y + 10y + x = 66

Simplifying this equation:

• 11x + 11y = 66
• x + y = 6

The second condition states that the digits differ by 2, so we have the equation:

• x - y = 2 or y - x = 2

We have two possible equations to consider:

1. x + y = 6
2. x - y = 2

or

1. x + y = 6
2. y - x = 2

By solving these pairs of equations, we find that the following two-digit numbers satisfy both conditions: 27 and 45. Thus, there are two such numbers.