Answer:
The number of runners that finished in first place , second place and third place are 7 , 13 and 10 respectively.
Step-by-step explanation:
Let the no. of runners fished at first place be x
Let the no. of runners fished at second place be y
Let the no. of runners fished at third place be z
We are given that Lakeland High School had 30 individual- event placers
So, x+y+z=30 -----1
First-place finishers score 7 points
So, Total score of x runners = 7x
Second-place finishers score 4 points
So, total score of y runners = 4y
Third-place finishers score 1 point.
So, total score of z runners = z
We are given that 30 individual- event placers score a total of 111 points
So, 7x+4y+z=111 ----2
We are also given that The number of first- and second-place finishers was twice the number of third-place finishers.
x+y=2z ---3
Substitute the value from 3 in 1
x+y+z=30
2z+z=30
z=10
Substitute the value of z in 1 and 2
x+y=20 ----4 and 7x+4y=101 ---5
Substitute the value of x from 4 in 5
7(20-y)+4y=101
140-7y+4y=101
140-3y=101
39=3y
`13=y
Substitute the value of y and z in 1
x+13+10=30
x=7
Hence the number of runners that finished in first place , second place and third place are 7 , 13 and 10 respectively.
