SOLUTION: 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. Determine the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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. Determine the      Log On


   

Question 155052: 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. Determine the linear equation that will represent the number of children who will enroll at a given fee.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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. Determine the linear equation that will represent the number of
children who will enroll at a given fee
:
We need two sets of coordinates to make a linear equation.
:
The first set is given; call it: x1 = 250, y1 = 120
;
We can make a 2nd set using the information given, if we decrease the fee to
$200, that will increase the no. of children to 130. (5 for each $25 decrease)
Call these coordinates: x2=200, y2 = 130
:
Find the slope by using the slope formula: m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29
m = %28%28130-y120%29%29%2F%28%28200-250%29%29 = m = %28%2810%29%29%2F%28%28-50%29%29
m = -.2
:
Find the equation using the point/slope formula: y-y1 = m(x-x1)
y - 120 = -.2(x - 250
y - 120 - -,2x + 50
y = -.2x + 50 + 120
y = -.2x + 170 is our equation
:
Check this out; substitute 200 for x and confirm that y = 130