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Find all two - digit numbers with the following property: the difference of the number and the number with the same digits in reverse order is 54.

User Fuzzyalej
by
8.4k points

1 Answer

5 votes

Answer:

17

26

35

44

53

62

71

80

Explanation:

Let's solve the problem step by step.

Let's assume the two-digit number is represented as "AB," where A represents the tens digit and B represents the units digit. According to the problem, the difference between the number "AB" and the number "BA" is 54.

So, we have the equation:

(10A + B) - (10B + A) = 54

Simplifying the equation, we get:

9A - 9B = 54

Dividing both sides of the equation by 9, we have:

A - B = 6

Now, we need to find two-digit numbers where the difference between the tens digit and the units digit is 6. The possible combinations are:

(1, 7)

(2, 8)

(3, 9)

(4, 10) - But 10 is not a valid unit digit since it exceeds the range of a two-digit number.

So, the valid two-digit numbers that satisfy the given condition are:

17

26

35

44

53

62

71

80

Therefore, there are 8 two-digit numbers that have a difference of 54 when subtracted from the number formed by reversing their digits.

User Robo Mop
by
7.8k points