SOLUTION: Need assistance with a complex problem. 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

Question 140719: Need assistance with a complex problem.
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. 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. Graph the linear equation that represents the number of children who will enroll at a given fee.
Approximately how many students will enroll if the camp fee is $180? Round to the nearest child. Show all work for full credit. Approximately how many students will enroll if the camp is free?
I would be greatful for any assistance with this complexed problem.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the number of children (n) is a function of the fee (f), so n=mf+b

the slope (m) is the change in n (+10) divided by the change in f (-20), so m=10/(-20) or -1/2

to find b, use the given point (100 children, $250 fee)
__ substituting __ 100=(-1/2)(250)+b __ 100=-125+b __ 225=b

so the equation is n=(-1/2)f+225

f is the independent variable, graphed on the horizontal (x) axis

n is the dependent variable (depends on f), graphed on the vertical (y) axis

for a $180 fee __ n=(-1/2)180+225 __ n=-90+225 __ n=135
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