In last weekend's track meet, Lakeland High School had 30 individual- event placers score a total of 111 points. First-place finishers score 7 points, second-place finishers score 4 points, and third-place finishers score
1 point. The number of first- and second-place finishers was twice the
number of third-place finishers. Find the number of runners that finished in
each place.

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.

10

step-by-step explanation: