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Question 140997: The director of a summer day cmp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll.
Determine the linear equation tha will represent the number of children who will enroll a a given fee.
Graph the linear equatin that rpresens the number of children who will enroll at a given fee.
How many students will enroll if the camp fee is 180.00?
How many studens will enroll if the camp is free?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The director of a summer day camp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll.
Determine the linear equation that will represent the number of children who will enroll a a given fee.
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Let x = cost per child
Let y = no. of children enrolled
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From the information given, derive two set of x/y coordinates
100 kid at $250: x1=250, y1=100
and
110 kids at $230: x2=230, y2=110
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Find the slope using the slope equation: m = 
m =  = 
m = 
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Use the point/slope equation: y -y1 = m(x-x1)
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y - 100 = (x - 250)
y - 100 = x + 125
y = x + 125 + 100
y = x + 225; is the linear equation
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Graph the linear equation that represents the number of children who will enroll at a given fee.
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Graph y = x + 225,
To graph this, use an x scale of 0 to +450, and y scale from 0 to 300
(we are not interested in any neg values here)
You only need two pair of coordinates to plot a linear (straight line) graph
However here are three sets: we will find y for x = 100, x = 200, x = 250
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Substitute 100 for x, in the equation y = -.5x + 225 and find y
y = -.5(100) + 225
y = -50 + 225
y = +175
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If we were making a table for x/y values, it would be:
x | y
-------
100|175
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Substitute 200 for x and find y:
y = -.5(200) + 225
y = -100 + 225
y = +125
now our table is:
x | y
-------
100|175
200|125
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Substitute 250 for x, find y
y = -.5(250) + 225
y = -125 + 225
y = +100
we have:
x | y
-------
100|175
200|125
250|100
0 |225, note this is the y intercept (the camp is free, 225 kids)
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Plot these 4 points, join them with straight lines
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it should look like this:
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How many students will enroll if the camp fee is 180.00?
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substitute 180 for x in our equation and find y
y = (180) + 225
6 = -90 + 225
y = +135 will enroll
;
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How many students will enroll if the camp is free?
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In this case x = 0
y = (0) + 225
y = 225 enrolled if it is free, you can see on the graph, that's the y intercept
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did this make sense to you, any questions?
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