SOLUTION: The coach and the players of the football team shared the expense of a bus trip to a professional game. When 5 players were unable to go, each person had to pay an additional $1.50

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Question 449535: The coach and the players of the football team shared the expense of a bus trip to a professional game. When 5 players were unable to go, each person had to pay an additional $1.50 to cover the cost of $540. How many people made the trip?
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = original number of players + coach
+540%2Fx = original amount each had to pay
+540+=+%28540%2Fx+%2B+1.5%29%2A%28x-5%29+
+540+=+540+%2B+1.5x+-+2700%2Fx+-+7.5+
+2700%2Fx+%2B+7.5+=+1.5x+
+2700+%2B+7.5x+=+1.5x%5E2+
+1.5x%5E2+-+7.5x+-+2700+=+0+
+x%5E2+-+5x+-+1800+=+0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-1800%29+%29%29%2F%282%2A1%29+
x+=+%28+5+%2B-+sqrt%28+25+%2B+7200+%29%29+%2F+2+
x+=+%28+5+%2B-+sqrt%28+7225+%29%29+%2F+2+
x+=+%28+5+%2B+85%29+%2F+2+ ( can't use negative square root )
+x+=+45+
+x+-+5+ people made the trip
+45+-+5+=+40+
40 people made the trip
check:
+540+=+%28540%2Fx+%2B+1.5%29%2A%28x-5%29+
+540+=+%28540%2F45+%2B+1.5%29%2A%2845-5%29+
+540+=+%28+12+%2B+1.5%29%2A+40+
+540+=+13.5%2A40+
+540+=+540+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The coach and the players of the football team shared the expense of a bus trip to a professional game.
When 5 players were unable to go, each person had to pay an additional $1.50 to cover the cost of $540.
How many people made the trip?
:
Let x = no. which actually made the trip
then
(x+5) = no. planned to make the trip
Now we can say:
540%2Fx = actual cost per person
and
540%2F%28%28x%2B5%29%29 = planned cost per person
:
actual cost - planned cost = $1.50
540%2Fx - 540%2F%28%28x%2B5%29%29 = 1.5
:
Multiply by x(x+5)
x(x+5)*540%2Fx - x(x+5)540%2F%28%28x%2B5%29%29 = 1.5x(x+5)
:
Cancel the denominators, resulting in:
540(x+5) - 540x = 1.5x^2 + 7.5x
540x + 2700 - 540x = 1.5x^2 + 7.5x
:
540x's cancel
2700 = 1.5x^2 + 7.5x
:
A quadratic equation
1.5x^2 + 7.5x - 2700 = 0
;
Simplify, divide thru by 1.5
x^2 + 5x - 1800 = 0
;
Factors to
(x+45)(x-40) = 0
the positive solution is all we want here
x = 40 persons actually went
:
:
Check this
540/40 - 540/45 =
13.50 - 12.00 = $1.50 difference