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?
7 years ago
11 months ago
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.