The original number is 4 and 7
Let the unknown numbers be x and y
If the sum of the digits of a two-digit number is 11, hence;
- x + y = 11
- x = 11 - y ,........................... 1
If the digits are reversed and increased by 27, this is expressed as:
- 10y + x = 10x + y + 27 ........................2
Substitute equation 1 into 2 to have:
10y + x = 10x + y + 27
10y + 11 - y = 10(11-y) + y + 27
9y + 11 = 110-10y + y + 27
9y + 11 = 137 - 9y
9y + 9y = 137 - 11
18y = 126
y = 126/18
y = 7
Recall that x + y = 11
x = 11 - y
x = 11 - 7
x = 4
This shows that the original number is 4 and 7
Learn more about simultaneous equations: https://brainly.com/question/21654746
