Question

The sum of the digits of a certain two-digit number is 11. When you reverse its digits you decrease the number by 27. Find the number.Let x represent.Let y represent System:

a) x = 7, y = 4
b) x = 8, y = 3
c) x = 6, y = 5
d) x = 9, y = 2

Answer 1

The two-digit number where the sum of the digits is 11 and reversing the digits decreases the number by 27 is 74.

Step-by-step explanation:

The sum of the digits of a certain two-digit number is 11. When you reverse its digits you decrease the number by 27. We can form the equations x + y = 11 (since the sum of the digits is 11) and 10y + x = 10x + y - 27 (since reversing the digits decreases the number by 27, where 10x + y is the original number and 10y + x is the reversed number).

Using the first equation, we substitute x = 11 - y into the second equation:

10y + (11 - y) = (10(11 - y) + y) - 27

This simplifies to 9y + 11 = 110 - 9y - 27, which becomes 18y = 72, giving us y = 4. Substituting back into x = 11 - y, we get x = 7.

Therefore, the original number is 74, and the reversed number is 47, which is 27 less than 74, confirming our solution.