A two digit number is 4 times the sum of its two digits. The number that is…

To find the two-digit number shown in image_8cd9fb.png, we can represent the number as 10x + y, where x is the tens digit and y is the units digit.

Step-by-Step Calculation
Condition 1: The number is 4 times the sum of its digits.

10x + y = 4(x + y)

10x + y = 4x + 4y

6x = 3y, or y = 2x

Condition 2: The reversed number (10y + x) is 27 more than the original number.

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

9y - 9x = 27

y - x = 3

Solve the system of equations:

Substitute y = 2x into the second equation: 2x - x = 3

x = 3

Find y: y = 2(3) = 6

The number is 10(3) + 6 = 36.