SOLUTION: Please help....word problems are the death of me!!!! The sum of three numbers is 1. If the second number is subtracted from the sum of the first and third numbers, the result is -

Question 1130574: Please help....word problems are the death of me!!!!
The sum of three numbers is 1. If the second number is subtracted from the sum of the first and third numbers, the result is -1. If the third number is subtracted from the sum of the first and second numbers, the result is -9. Find the three numbers.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
First, second, third numbers
x, y, z

The description becomes
which can be solved using minimal skills.

Look at the last two equations carefully. what happens if you add them?

, and you can use or choose other methods to get y and z.
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

Let the numbers be x, y and z. Then the problem says x + y + z = 1 (1) x - y + z = -1 (2) x + y - z = -9 (3) Do not be afraid. Simply subtract equation (2) from equation (1). The terms "x" and "z" will cancel each other and you will get 2y = 1 - (-1) = 2 =====> y = 2/2 = 1. Next subtract equation (3) from equation (1). The terms "x" and "y" will cancel each other and you will get 2z = 1 - (-9) = 10 =====> z = 10/2 = 5. As the last step, substitute y= 1 and z= 5 into equation (1). You will get x + 1 + 5 = 1 =====> x = -5. Answer. x= -5; y= 1; z= 5.

Solved.

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