the sum of the digits of a three digit number is12. the tens digit is 2 lessthan the hundreds digit, and the units digit is 4 less than the sum of the two digits. What is the number?

534

To find the number, we need to follow the given conditions step by step.

Let's start by assigning variables to the digits of the three-digit number. We'll represent the hundreds digit as 'H,' the tens digit as 'T,' and the units digit as 'U.'

Condition 1: The sum of the digits is 12. So, we have the equation:

H + T + U = 12 ----(1)

Condition 2: The tens digit is 2 less than the hundreds digit. This gives us the equation:

T = H - 2 ----(2)

Condition 3: The units digit is 4 less than the sum of the two digits. This gives us the equation:

U = H + T - 4 ----(3)

Now, we have a system of three equations (1), (2), and (3), which we can solve simultaneously to find the values of H, T, and U.

Substitute equation (2) into equation (3) to eliminate T:
U = H + (H - 2) - 4
U = 2H - 6 ----(4)

Substitute equations (2) and (4) into equation (1) to eliminate T and U:
H + (H - 2) + (2H - 6) = 12
4H - 8 = 12
4H = 20
H = 5

Now, substitute the value of H into equation (2) to find T:
T = 5 - 2
T = 3

Finally, substitute the values of H and T into equation (3) to find U:
U = 5 + 3 - 4
U = 4

Therefore, the three-digit number is 534.