Question

In an interschool atheletic meet, with 24 individual events, securing a total of 56 points, a first place secures 5 points, a second place secures 3 points, and a third place secures 1 point. Having as many third place finishers as first and second place finishers, find how many athletes finished in each place

Answer 1

Answer:

In an interschool atheletic meet, with 24 individual events, securing a total of 56 points, a first place secures 5 points, a second place secures 3 points, and a third place secures 1 point. Having as many third place finishers as first and second place finishers, find how many athletes finished in each place.

Please explain me each n every step

Answer 2

Step-by-step explanation:

Let the number of I, II and III place finishers be z, y and z respectively. Total number of events = 24; Total number of points = 56.

Hence, the linear equations in three variables are r+ y +: = 24 ...(1)

5x + 3y + = 56 ...(2)

Substituting (3) in (1) we get, : +2

.. (3) will be, a+y = 12

(2) =

3x(3) =

= 24 => z=12

5x + 3y = 44 (-)

3r +3y = 36

2.r

= 8

we get, I = 4

Substituting r = 4, z= 12 in (3) we get, y = 12 - 4 = 8 Therefore, Number of first place finishers is 4

Number of second place finishers is 8 Number of third place finishers is 12.