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?

2 Answers
Sep 28, 2015

Answer:

#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#

Sep 28, 2015

Answer:

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.