SOLUTION: Hi, Can anyone solve this problem? The sum of three numbers is 9. The first minus the second, plus the third is 3. The first minus the third is 1 more than the second. What are th

What you are given is 

x + y + z = 9,    (1)
x - y + z = 3,    (2)
x - z = y + 1.    (3)

Modify (3):

x - y - z = 1.    (3')

Add equations (1) and (3') (both sides). You will get

2x = 9 + 1,   or   2x = 10,   hence,   x =  = 5.

Add equations (1) and (2). You will get

2x + 2z = 12.      (4)

Since x = 5, it gives 2*5 + 2z = 12,   or   2z = 12 - 10,   or 2z = 2,   and then  z = 1.

Finally, from (1) y = 9 - x - z = 9 - 5 - 1 = 3.

Answer.  x = 5,  y = 3  and  z = 1.

Check it yourself.

Let the 1st, 2nd, and 3rd, be F, S, and T, respectively

Then we get the following:

                F + S + T = 9 ------ eq (i)

                F – S + T = 3 ------ eq (ii)

F – T = S + 1___F – S – T = 1 ------ eq (iii)

                       2T = 2 ------ Subtracting eq (iii) from eq (ii) 

T, or 3rd number = , or 



2F = 10 ---------- Adding eqs (iii) & (i)

F, or 1st number = , or 



5 + S + 1 = 9 ------- Substituting 1 for T, and 5 for F in eq (i)

6 + S = 9

S, or 2nd number = 9 – 6, or