Problema Solution
The swim team placed 27 swimmers at a recent invitational. First place was worth 5 points, second place was worth 3 points and third place was worth 1 point. The team totaled 85 points, and the number of first place finishers was three less than the number of second and third place finishers combined. How many swimmers finished in either first, second, or third place?
Answer provided by our tutors
5 f + 3 s + t = 85
f = s+ t - 3
f+s+t = 27 = 2 f + 3 = 27 = > f = 12
using eq 2 in eq 1
5s + 5t-15 + 3s + t = 85
8s+6t = 100 = > 4s + 3t = 50 --- eq4
s+t = 15 (multiply this by 4)
4s + 4t = 60 --eq(5)
deducting eq4 from eq5
t = 10
s = 5