what is the number?

Question

translate the problem into a system of 3 equations using 3 variables. solve the system. the sum of the digits of a three-digit number is 12. the tens digit is 2 less than the hundreds digit, and the units digit is 4 less than the sum of the other two digits.

Answer 1

Write:

h + t + o = 12

h − 2 = t

h + t − 4 = o

In h + t + o = 12, replace t with h − 2 and replace o with h + t − 4.

Then h + h − 2 + h + t − 4 = 12 or 3h + t = 18 or t = 18 − 3h which equals h − 2.

Next, 18 − 3h − h + 2 = 0 or 20 − 4h = 0 and h = 5. This gives t = 5 − 2 or 3. Finally,

o = 5 + 3 − 4 or 4. The three-digit number sought is then 534.