SOLUTION: 5. The director of a summer day camp estimates that 120 children will join if the camp fee is $250, but for each $25 decrease in the fee, five more children will enroll. A.

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Question 122431: 5. The director of a summer day camp estimates that 120 children will join if the camp
fee is $250, but for each $25 decrease in the fee, five 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 $190? Round to the nearest child. Show all work to receive full credit.
D. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work to receive full credit.

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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The director of a summer day camp estimates that 120 children will join if the
camp fee is $250, but for each $25 decrease in the fee, five 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.
:
Since the no. of kids depend on the cost; let x = cost; y = no. of kids
Derive two points:
x1 = 250; y1 = 120; given
x2 = 200; y2 = 130; Given that a $50 reduction increases kids by 10
:
Find the slope from this:
m = %28130+-+120%29%2F%28200+-+250%29 = 10%2F%28-50%29 = -.2 is the slope
:
Find the equation using the point/slope formula:
y - 120 = .2(x - 250)
y - 120 = -.2x + 50
y = -.2x + 50 + 120
y = -.2x + 170; this is linear equation
:
B. Graph the linear equation that represents the number of children who will enroll at a given fee.
:
Plot the two given sets of points and draw the graph, it should look like this:
+graph%28+300%2C+200%2C+-100%2C+400%2C+-20%2C+200%2C+-.2x%2B170%29+
:
C. Approximately how many students will enroll if the camp fee is $190? Round to the nearest child. Show all work to receive full credit.
:
Using our equation, substitute 190 for x and find y
y = -.2(190) + 170
y = -38 + 170
y = + 132 children at this $190
:
:
D. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work to receive full credit.
:
you can see by the graph, and the equation, that when x = 0 and y = 170
:
170 children if it's free.