SOLUTION: Please help me solve this word problem Adams High prevailed in a track meet with the help of 20 individual-event placers earning a combined 68 points. A first-place finish earn

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Question 1159591: Please help me solve this word problem
Adams High prevailed in a track meet with the help of 20 individual-event placers earning a combined 68 points. A first-place finish earns 5 points, a second place finish earns 3 points, and a third-place finish earns 1 point. Adams had a strong second place showing, with as many second-place finishers as first-and third place finishers combined. Use a system of linear equations to model the data. Solve the system to find how many athletes finished in each place.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
F+S+T=20
5F+3S+1T=68
but S=F+T
so the first may be written as
2F+2T=20
and the second as
8F+4T=68
-4F-4T=-40 multiplying the top by -2
4F=28
F=7 first places and 35 points
Now there is S+T=13
and 3S+1T=33 (points left)
and -S-T=-13
2S=20
S=10 second places
T=3 third places
!st place--7
2nd place-10
3rd place--3