Question

The number of football players is 4 times the number of basketball players, and the number of baseball players is 9 more than basketball players. If the total number of players is 93 and each one plays a single sport, how many are on each team?

Answer 1

`56` football players
`14` basketball players
`23` baseball players

Explanation:

Define:
`color(white)("XXX")f:`number of football players
`color(white)("XXX")b:`number of basketball players
`color(white)("XXX")d:`number of baseball players

We are told:
[1]`color(white)("XXX"color(red)(f=4b)`
[2]`color(white)("XXX")color(blue)(d=b+9)`
[3]`color(white)("XXX")f+b+d=93`

Substituting (from [1]) `color(red)(4b)` for `color(red)(f)` and (from [2]) `color(blue)(b+9)` for `color(blue)(d)` in [3]
[4]`color(white)("XXX")color(red)(4b)+b+color(blue)(b+9) = 93`

Simplifying
[5]`color(white)("XXX")6b+9 = 93`
[6]`color(white)("XXX")6b=84`
[7]`color(white)("XXX")b=14`

Substituting `14` for `b` in [2]
[8]`color(white)("XXX")d=14+9 = 23`

Substituting `14` for `b` in [1]
[9]`color(white)("XXX")f=4*14 = 56`

Answer 2

56 football players, 14 basketball players, and 23 baseball players.

Explanation:

Let the number of football players be x
Let the number of basketball players be y
Let the number of baseball players be z

Now rewrite all the sentences in algebraic form in terms of x, y and z. Doing so we get :

`x=4y`
`z=y+9`
`x+y+z=93`

Now we can substitute both x and z (which we have in terms of y) into the last equation and then solve for y. This yields

`4y+y+(y+9)=93`

`therefore 6y=84=>y=14` and so there 14 basketball players.

Now substitute the value of y back into the first 1 equations to determine x and z.
`therefore x=4xx14=56 and z=14+9=23`
This means there are then 56 football players and 23 baseball players.