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?
:
Let x = no. which actually made the trip
then
(x+5) = no. planned to make the trip
Now we can say:
{{{540/x}}} = actual cost per person
and
{{{540/((x+5))}}} = planned cost per person
:
actual cost - planned cost = $1.50
{{{540/x}}} - {{{540/((x+5))}}} = 1.5
:
Multiply by x(x+5)
x(x+5)*{{{540/x}}} - x(x+5){{{540/((x+5))}}} = 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