4. In yesterday's swim meet Roosevelt High dominated in the individual events, with 24 individual swimmers scoring a total of 56 points for Roosevelt High. A first place finish scores 5 points, a second place finish scores 3 points and a third place finish scores 1 point There were as many third place finishers as first and second place finishers combined. How many first place, second place, and third place finishers were there? Write, then solve a system of equations to model the information above.

Question

Answer 1

To solve this problem, we need to set up a system of equations based on the information given.Let's define:-

as the number of first place finishers,-

as the number of second place finishers,-

as the number of third place finishers.From the problem, we have the following information:1. The total number of swimmers is 24:

2. The total points scored is 56, with first place scoring 5 points, second place scoring 3 points, and third place scoring 1 point:

3. There were as many third place finishers as first and second place finishers combined:

Now, we have a system of three equations:

We can substitute equation (3) into equations (1) and (2):Substitute

into equation (1):

Now substitute

into equation (2):

Now we have a simpler system of two equations:

We can solve this system using substitution or elimination. Let's use substitution:From equation (1), express

in terms of

:

Substitute

into equation (2):

Now substitute

back into

:

Finally, use equation (3) to find

:

Thus, there are 4 first place finishers, 8 second place finishers, and 12 third place finishers.

Question