SOLUTION: A group of teachers plan a tour in their province.The total fare is 1200 which is to be shared equally among them.If two more teachers join the tour each will pay 20 less.Find the

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Question 762392: A group of teachers plan a tour in their province.The total fare is 1200 which is to be shared equally among them.If two more teachers join the tour each will pay 20 less.Find the original number of teachers in the group.
Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website!
Let A = number of teachers.

Multiply everything by A and (A+2)

Simplify the equation.

Multiply through.

Subtract 1200A from both sides.

Subtract 2400 from both sides.

I divide everything by 20 just to reduce the size of the numbers.

Now use the quadratic equation to solve for X.

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=484 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10, -12. Here's your graph:

A = 10 & -12
Since we can not have a negative number of people, A = 10
There were 10 teachers.