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The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third number is nine. The difference between the second number and half the third is 10. Find the numbers.

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jafransp

Answer:

The numbers are 3, 5, -10.

Step-by-step explanation:

Let, the numbers are X, Y, Z.

Given, sum of the three numbers are -2.  

So, the equation is X + Y+ Z = -2 .......(i)

Again, for 2nd condition, the equation will be  

3X + 2Y + Z = 9  ....... (ii)

Again, for the third condition, the equation will be

Y - (Z/2) = 10 ......(iii)

Multiplying the equation (i) by 3 and the equation (ii) by 1, we get

                     3X + 3Y+ 3Z = -6

                     3X + 2Y +  Z =  9

(Deduct)                  Y + 2Z = -15 ......(iv)  

Solving equation (iii) and (iv) we get,

                         Y - (Z/2) = 10

                         Y + 2Z   = -15

(Deduct)        -(Z/2) - 2Z = 25

or, (-Z-4Z)/2 = 25

or, -5Z = 25*2

or, Z = 50/(-5)

Therefore, Z = -10

Putting the value of Z into equation (iv) we get,

Y + 2*(-10) = -15

or, Y - 20 = -15

or, Y = 20 - 15

Therefore, Y = 5

Putting the value of Y and Z into equation (i) we get,

X + 5 + (-10) = -2

or, X + 5 - 10 = -2

or, X - 5 = -2

or, X = 5 - 2

Therefore, X = 3

So, the numbers are, X = 3; Y = 5; and Z = -10.