If a company has total costs
C(x) = 35,000 + 45x + 0.2x2
and total revenues given by
R(x) = 615x − 0.8x2,
find the break-even points.

The break-even points are:  x = 500, and x = 70

Step-by-step explanation:

The break even points are those x-values for which the Revenue equals the Cost, so there is no money lost.

Since the formulas for both Revenue and Cost are given, we find the breaking  points by setting the functions equal to each other:

where we have gathered all terms on one side of the equation and written the equation in standard form.

We can use the quadratic formula to solve for "x":

 has solutions given by:

In our case,  

So the solutions are:

This leads to two solutions:

These are the break-even points.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.