The sum of the digits of a two-digit number is 16. If the digits are reversed the new number will be 18 greater than the original number. Find the number.

By trial and error, I found that three numbers meet the first criteria: 88, 79, 97.

Which of those numbers meets the second criteria?

79

Let A = the first digit and B + the second digit.

Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

Therefore, A + B = 16 and 97 - 79 = 17.

Sorry for the mental error. The hand was slower than the eye.

Let A = the first digit and B + the second digit.

Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

Therefore, A + B = 16 and 97 - 79 = 18

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To find the two-digit number, let's assign variables to the tens and ones digits. Let's call the tens digit "x" and the ones digit "y".

According to the given information, the sum of the digits is 16. This can be written as the equation: x + y = 16.

We are also told that when the digits are reversed, the new number is 18 greater than the original number. This can be written as the equation: 10y + x = 10x + y + 18.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From the first equation, we can rewrite it to x = 16 - y.

Substituting x = 16 - y in the second equation, we get: 10y + (16 - y) = 10(16 - y) + y + 18.

Simplifying the equation: 10y + 16 - y = 160 - 10y + y + 18.

Combining like terms: 9y + 16 = 160 - 9y + 18.

Further simplifying: 9y + 16 = 178 - 9y.

We can then add 9y to both sides of the equation: 18y + 16 = 178.

Next, subtract 16 from both sides: 18y = 162.

Finally, divide both sides by 18: y = 9.

Substituting the value of y = 9 into the first equation x + y = 16, we get: x + 9 = 16.

Subtracting 9 from both sides: x = 7.

Therefore, the tens digit (x) is 7, and the ones digit (y) is 9.

The original number is 79.