sum of three numbers is -2

Question

The sum of three times the first number,twice the second number,and the third number is 9.The difference between the second number and half the third number is 10.Find the numbers

Answer 1

If the numbers are a, b and c, then:

a+b+c=-2, so 3a+3b+3c=-6 (1)

3a+2b+c=9 (2)

b-c/2=10, b=10+c/2 (3)

(1)-(2)=b+2c=-15, b=-15-2c, therefore 10+c/2=-15-2c, 25=-5c/2, c=-(2/5)25=-10.

And b=10-10/2=5, and a=-2-(b+c)=-2-(5-10)=-2+5=3.

CHECK

a+b+c=3+5-10=-2 OK.

3a+2b+c=3×3+2×5-10=9 OK.

b-c/2=5-(-5)=5+5=10 OK.

SOLUTION: a=3, b=5, c=-10.