HI HELP..........math is my nightmare?

Question

5. The director of a summer day camp estimates that 100 children will join if the camp fee is $250, but for each $20 decrease in the fee, ten more children will enroll.

A. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the line. Show all work to receive full credit.






B. Graph the linear equation that represents the number of children who will enroll at a given fee.




C. Approximately how many students will enroll if the camp fee is $180? Round to the nearest child.




D. Approximately how many students will enroll if the camp is free? Round to the nearest child.

Answer 1

Let C be the number of children, and F be the fee.
We're given the point (C,F): (100, 250)
We also know that if the fee decreases by $20, ten more children will enroll.
That gives us the point: (110, 230).

A.) We'll use these two points to find the equation, using the point-point form.
(x - x1)/(y - y1) = (x2 - x1)/(y2 - y1)
Or in this case:
(C - C1)/(F - F1) = (C2 - C1)/(F2 - F1)
(C - 100)/(F - 250) = (110 - 100)/(230 - 250)
(C - 100)/(F - 250) = 10/(-20)
(C - 100)/(F - 250) = -1/2
2C - 200 = -F + 250
F = -2C + 450

B.) I hope you know how to graph a line given two points. Just choose your units judiciously so it doesn't run off the paper.

C.) F = -2C + 450
180 = -2C + 450
2C = 450 - 180
C = 270/2 = 135 students

D.) 0 = -2C + 450
2C = 450/2 = 225 students