SOLUTION: I have been battling with this problem for over a two hours if someone could please help me. The sum of nine times the first number and five times a second number is 24. The se

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Question 283593: I have been battling with this problem for over a two hours if someone could please help me.
The sum of nine times the first number and five times a second number is 24. The second number is seventeen less than twice the first. Find the two numbers.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
So what have you tried?
let a = one number
b=other number
....+.......9.....*.........a............+...5....*.........b.........=..24
The sum of nine times the first number and five times a second number is 24
9a+5b=24
........b..........= 17..........-........2a
......................17 less than =-17
The second number is seventeen less than twice the first.
b=-17+2a
b=2a-17
b+17=2a
(b+17/2)=a
b=2a-17
9a+5b=24
I suspect there is a problem with the problem.
Double check the numbers.
a = 109/19, b = -105/19
a is about 5.7 and b is about -5.5

b=2a-17
-105/19=2*109/19-17
(218-105)/19=17
113/19=17
ok
9a+5b=24
9*109/19+5*-105/19=24
981/19=525/19=24
456/19=24
456=24*19
ok
My answers work. I just don't like them.
And I don't see anything wrong with the equations.