the sum of the digits of a two digit number is 15. if the digits are reversed, the new number is 27 less than the original number. find the original number.
Accepted Solution
A:
Define original value of the two digit I make an example, a is the first digit and b is the second digit. The original value of the digit will be 10a + b because a stands as tens and b stands as units
Make an equation system The sum of two digit is 15 ⇒ a + b = 15 (this is first equation) If the digits are reversed, the new number is 27 less than the original number. That means b will stand as tens, and a will stand as units. ⇒ 10b + a = (10a + b) - 27 (this is second equation)
Solve the equation To find the numbers, we should solve the first and second equation. From the first equation a + b = 15 a = 15 - b
Subtitute 15 - b to a in the second equation 10b + a = 10a + b - 27 10b + (15 -b) = 10(15 - b) + b - 27 9b + 15 = 150 - 10b + b - 27 9b + 10b - b = 150 - 27 - 15 18b = 108 b = 6
Subtitute 6 as b to the first equation a = 15 - b a = 15 - 6 a = 9