both my hundreds and units digits are one-half of my tens digit.the sum of my three digits is 16. what am i?
x y z
x = .5 y
z = .5 y
x + y + z = 16
.5 y + y + .5 y = 16
2 y = 16
y = 8
so
484
To find the number that satisfies the given conditions, let's work through the problem step by step:
Let's assume the tens digit is x. Since the hundreds and units digits are both one-half of the tens digit, we can express them as (x/2).
According to the problem, the sum of the three digits equals 16. So we can write the equation:
x + (x/2) + (x/2) = 16
Let's simplify this equation:
2x/2 + x/2 + x/2 = 16
(2x + x + x)/2 = 16
4x/2 = 16
2x = 16
x = 8
Now we know that the tens digit is 8.
To find the hundreds digit, we multiply the tens digit by one-half:
Hundreds digit = 8/2 = 4
To find the units digit, we also multiply the tens digit by one-half:
Units digit = 8/2 = 4
Therefore, the number that satisfies all the given conditions is 484.