Question 95752

Let 100x= the hundreds digit
10y=the tens digit 
And z=the units digit

Now we are told that x+y+z=15-------------------eq1

We are also told that: 
y=z+1-----------------------------------------------eq2

We are further told that:
x+z=9-----------------------------------------------eq3

In eq3, subtract z from both sides:
x+z-z=9-z collect like terms
x=9-z-----------------------------------------eq3

Next, add eq2 and eq3 and we get:
x+y=10 Now substitute x+y=10 into eq1

10+z=15  subtract 10 from both sides
10-10+z=15-10  collect like terms

z=5-------------------------------units digit
From eq2, y=z+1=5+1=6-----------------------tens digit

From eq3, x=9-z=9-5=4-----------------------------hundreds digit

So our three digit number is: 465

CK
4+6+5=15 ok
15=15
y=z+1
6=5+1 ok
x+z=9
5+4=9
9=9 ok

Hope this helps---ptaylor