The sum of digit in two-digit number is 13. If the place values of the digits are reversed，the new number is 27 more than the original number。Find the original number。

Question

The sum of digit in two-digit number is 13. If the place values of the digits are reversed，the new number is 27 more than the original number。Find the original number。

Answer 1

This problem can be solved by creating two equations with two unknowns and solving them using elimination (or substitution).

In the first number, let's use the variable x to represent the first digit in the number and the variable y to represent the second digit in the number.

Then we can write the following equation to represent the info provided in the first sentence:

13 = x + y

Using the concept that the digit in the tens place actually represents 10 times the digit and the digit in the ones place represent 1 times that digit, we can write the following equation using the rest of the information provided:

10x + 1y + 27 = 10y + 1x

We can rearrange this equation and combine like terms to create the following:

27 = -10x -1y + 10y + 1x

27 = -9x + 9y

Now we can combine the following equations and solve for y (the digit in the ones place in the first number):

13 = x + y

27 = -9x + 9y

Let's multiply the first equation by 9 so that we can solve for y:

13 = x + y becomes 117 = 9x + 9y

Then combine:

117 = 9x + 9y

27 = -9x + 9y

144 = 18y

8 = y

Since the sum of the digits is 13, x will be 5.

The second number will be 85, the first number will be 58