SOLUTION: A group of friends planned a trip and chartered a bus for 300$. When 3 more friends decided to join the trip, the cost for the bus was $5 less per person. In all, how many people m

Question 697541: A group of friends planned a trip and chartered a bus for 300$. When 3 more friends decided to join the trip, the cost for the bus was $5 less per person. In all, how many people made the trip.
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
Set Up:
Let A = the number of friends in the begining.
Let B = the cost per person
-----------------------------
Equation 1:
Equation 2:
Plug (300/A) into equation 2 for B
Equation 2:

To simplify the equation, multiply both sides by (A+3)

Multiply both sides by A

Simplify

Combine like terms

Subtract 285A from both sides

Add 5A^2 to both sides

*This step is not required but to make the numbers smaller pull a 5 from the right side of the equation

Divide both sides by 5

Subtract 180 from both sides

Use the quadratic equation.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=729 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12, -15. Here's your graph:

Note that there are two answers; 12 & -15.
Now we can not have negative people so your only answer is 12.
That means that 12 people were the original group and then 3 more people joined.
So there were 15 total people that made the trip.

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