Question

Lawrence High prevailed in Saturday's 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. Lawrence had a strong
second-place showing, with as many second
place finishers as first and third-place
finishers combined.

Answer 1

The answer is below

Explanation:

Let x represent a first place finish, y represent a second place finish and z represent a third place finish.

Since there is a total of 20 individual events, hence:

x + y + z = 20 (1)

A first place finish is 5 point, a second place finish is 3 point and third place finish is 1 point. Therefore:

5x + 3y + z = 68 (2)

The second place finishers is as much as first and third-place finishers combined. Hence:

y = x + z (3)

Solving equation 1, 2 and 3 simultaneously gives:

x = 7, y = 10 and z = 3

This means the number of first place finishes was 7, second place finishes was 10 and third place finishes was 3