SOLUTION: Word Problems Define all variables Must set up equations and solve choosing best method. THIS QUESTION IS ABOUT USING 3 VARIABLE EQUATIONS. HERE IT IS The sum of three number

Question 165315: Word Problems Define all variables Must set up equations and solve choosing best method. THIS QUESTION IS ABOUT USING 3 VARIABLE EQUATIONS.
HERE IT IS
The sum of three numbers is 18. The third number is four times the second, and the second number is 6 more than the first. Find the numbers.
I got the answer using guess and check, but have no clue about how to write the equation.
Thank you
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Follow the directions given in the problem description:
First, assign variables to the three unknowns:
Let a = 1st number.
Let b = 2nd number.
Let c = 3rd number.
From the problem description, you can write:
1) a+b+c = 18 "The sum of three numbers is 18".
2) c = 4*b "The third number (c) is four times the second (4*b)"
3) b = a+6 "...the second number (b) is 6 more than the first (a+6)"
So now you have three equations with three unknowns.
Substitute the second equation (c = 4*b) into the first equation to get:
a+b+(4*b) = 18 Now rewrite the third equation as a = b-6 and substitute into the first equation to get:
(b-6)+b+4*b = 18 So now you have one equation with one unknown (b) and you can solve this for b.
b-6+b+4*b = 18 Combine like-terms:
6b-6 = 18 Add 6 to both sides.
6b = 24 Divide both sides by 6.
b = 4
From equation 2) you can find c.
c = 4*b
c = 4*4
c = 16
From the re-written equation equation 3, you can find a:
a = b-6
a = 4-6
a = -2
The three numbers are: -2, 4, 16
Check:
a+b+c = 18
(-2)+4+16 = (-2)+20 = 18.
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