the soccer club has planned a trip to a tournament. the cost of the van is $231 when 3 students who are not members of the club join the trip, the transportation cost per person drops by $4.50 how many soccer members are going to the tournament?
ticket price p = 231/n
p-4.5 = 231/(n+3)
231/n - 4.5 = 231/(n+3)
231(n+3)-4.5(n^2+3n) = 231 n
231*3 -4.5 n^2 - 13.5n = 0
4.5 n^2 + 13.5 n - 693 = 0
n = 11 or -14
so
11
===========================
check
231/11 = 21
231/14 = 16.5 yes, diff = 4.50
Let's assume the number of soccer club members going to the tournament is "x".
The original cost of transportation per person is given as $231.
When 3 non-members join the trip, the transportation cost per person drops by $4.50.
Therefore, the new cost of transportation per person would be $231 - $4.50 = $226.50.
We can create an equation to solve for "x":
Original cost per person = New cost per person when 3 non-members join.
231 / x = 226.50 / (x + 3)
To solve this equation, we can cross-multiply:
231(x + 3) = 226.50x
Expanding the equation results in:
231x + 693 = 226.50x
Subtracting 226.50x from both sides of the equation:
231x - 226.50x = 693
4.50x = 693
Dividing both sides by 4.50:
x = 154
Therefore, there are 154 soccer club members going to the tournament.
To find the number of soccer club members going to the tournament, we can use algebra. Let's represent the number of soccer club members as 'x'.
Given:
Cost of van without any additional students = $231
When 3 non-club members join the trip, the transportation cost per person drops by $4.50
If x represents the number of soccer club members going to the tournament, we can calculate the cost per person as follows:
Cost per person = Total cost of van / (Number of soccer club members + 3 non-club members)
According to the given information, the cost per person decreases by $4.50 when 3 non-club members join. This can be represented as:
Cost per person with x club members - Cost per person with x club members + 3 non-club members = $4.50
Now we can set up the equation and solve for x:
$231 / x - $231 / (x + 3) = $4.50
To simplify the equation, we can multiply both sides by x(x + 3) to eliminate the denominators:
$231(x + 3) - $231x = $4.50x(x + 3)
Now we have:
231x + 693 - 231x = 4.5x^2 + 13.5x
Simplifying further:
693 = 4.5x^2 + 13.5x
Rearranging the equation to make it equal to zero:
4.5x^2 + 13.5x - 693 = 0
To solve this quadratic equation, we can use either factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 4.5, b = 13.5, and c = -693. Plugging in these values:
x = (-13.5 ± √(13.5^2 - 4 * 4.5 * -693)) / (2 * 4.5)
Calculating further:
x = (-13.5 ± √(182.25 + 12474)) / 9
x = (-13.5 ± √12656.25) / 9
x = (-13.5 ± 112.5) / 9
Now we have two possible solutions:
1. x = (-13.5 + 112.5) / 9 = 99 / 9 = 11
2. x = (-13.5 - 112.5) / 9 = -126 / 9 = -14
Since the number of soccer club members cannot be negative, we discard the negative solution.
Therefore, the number of soccer club members going to the tournament is 11.