SOLUTION: A recreational softball team paid a league entry fee of $825. The cost was covered by equal contributions from each memeber on the team. If there were four more team members, each

Question 110213: A recreational softball team paid a league entry fee of $825. The cost was covered by equal contributions from each memeber on the team. If there were four more team members, each person could contibute $20 less. How many memebers does the team have?
i tried to write an equation... i made "x" be the money the players were contributing and "p" be the number of players
since it said the fee was split evenly, i put 825/x = p.
also, i had (p+4) = 825/(x-20) because if there were four more players they would have to pay $20 less than before. After that, i could understand how you were able to figure out how many members the team had. Could you help me please?
Thanks a lot tutor!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A recreational softball team paid a league entry fee of $825. The cost was covered by equal contributions from each memeber on the team. If there were four more team members, each person could contibute $20 less. How many memebers does the team have?
i tried to write an equation... i made "x" be the money the players were contributing and "p" be the number of players
since it said the fee was split evenly, i put 825/x = p.
also, i had (p+4) = 825/(x-20) because if there were four more players they would have to pay $20 less than before. After that, i could understand how you were able to figure out how many members the team had. Could you help me please?
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You have 825/x as the average cost per member at the start.
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You have 825/(x+4) as the average cost if there were 4 more members.
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EQUATION:
Old Average - New average = $20
825/x - 825/(x+4) = 20
4*825 = 20x(x+4)
825 = 5x(x+4)
165 = x(x+4)
x^2+4x-165 = 0
(x+15)(x-11)=0
x = 11 (original number of members)
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Cheers,
StanH.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You set up the problem correctly, except that I started with
:
The next step was to write:
:
Since and both equal the same thing, you can write:
:

:

:
, but we know that , so:
:
,

, which factors to:

:
Hence, or .
:
Throw out the negative result because you can't have a negative number of people on a team, and your answer is 11.
:
Check:

, 15 is 4 more than 11, and 55 is 20 less than 75. Check.
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