The sum of digits of a 3 digit number is 12. Three times the hundreds digit minus twice the tens digit is 5. If six time the units digit is added to four times the tens digit, the result is 50. Find the number.

So

xyz

x+y+z=12

3x-2y=5

6z+4y=50

so multiply 3x-2y=5 by 2

6x-4y=10

add to 6z+4y=50 and get

6x+6z+4y-4y=10+50

6x+6z=60

distribute

6 (x+z) = 6 (10)

divide both sides by 6

x+z=10

subsitute 10 for x+z in the first equation

10+y=12

y=2

subsitute

3x-2 (2) = 5

3x-4=5

3x=9

x=3

x+z=10

3+z=10

z=7

x=3

y=2

z=7

number is

327