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You mentioned that the digits of a two-digit number sum to 8, and when the digits are reversed, the resulting number is 18 less than the original number.

Let's use x for the tens digit and y for the ones digit. We have the following equations:

1. x + y = 8 (The sum of the digits is 8).

2. 10y + x = 10x + y - 18 (When the digits are reversed, the number is 18 less than the original).

Now, let's solve for x and y:

From the first equation (x + y = 8), we can express x as x = 8 - y.

Substitute this expression for x into the second equation:

10y + (8 - y) = 10(8 - y) + y - 18

Now, simplify the equation:

9y + 8 = 80 - 10y + y - 18

Combine like terms:

9y + 8 = 80 - 9y - 18

Add 9y to both sides:

18y + 8 = 62

Subtract 8 from both sides:

18y = 62 - 8

18y = 54

Now, divide by 18 to find y:

y = 54 / 18

y = 3

Now that we have found y, you can find x using the first equation:

x = 8 - y

x = 8 - 3

x = 5

So, the correct original two-digit number is 53.

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Let's the tens digit of the original number "x" and the ones digit "y". According to the problem, we have two equations:

x + y = 8 (the digits sum to 8)

10y + x = 10x + y - 18 (the reversed number is 18 less than the original)

we can use the information given. From the first equation, we have

• x + y = 8.

From the second equation, we have

• 10y + x = 10x + y - 18.

Let's simplify the second equation:

• 10y + x = 10x + y - 18
• 9y - 9x = -18
• y - x = -2

Now we have a system of equations:

• x + y = 8
• y - x = -2

By adding these two equations together, we can eliminate x:

• 2y = 6

Therefore, y = 3.

Substituting y = 3 into the first equation, we can find x:

• x + 3 = 8
• x = 5

So the original number is 53.

☆ Hope it's helpful ☆