SOLUTION: The sum of three numbers is 90 . The first number is 6 less than the second . The third number is 2 times the second. What are the numbers?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The sum of three numbers is 90 . The first number is 6 less than the second . The third number is 2 times the second. What are the numbers?       Log On


   

Question 639570: The sum of three numbers is 90 . The first number is 6 less than the second . The third number is 2 times the second. What are the numbers?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's numbers be x (the first), y (the second) and z (the third)
given:
The sum of three numbers is 90 .
x%2By%2Bz=90 ..............1
The first number is 6 less than the second .
x%2B6=y.............2
The third number is 2 times the second.

z=2y..............3
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solve this system:
x%2By%2Bz=90 .........1
x%2B6=y.............2
z=2y..............3.....plug in 1
_________________________
x%2By%2B2y=90 .........1...solve for x
x%2B3y=90
x=90-3y...........plug in 2
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90-3y%2B6=y.............2..solve for y
96=y%2B3y
96=4y
96%2F4=y
highlight%2824=y%29....now find x
x=90-3y
x=90-3%2A24
x=90-72
highlight%28x=18%29...now find z
z=2y..............3
z=2%2A24
highlight%28z=48%29