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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 the numbers?
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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.
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 the numbers?
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