SOLUTION: there are currently 20 members in a school's ski club and the dues are $8 per member. to encourage the recruiting of new members, the club treasurer suggests that for each new memb

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: there are currently 20 members in a school's ski club and the dues are $8 per member. to encourage the recruiting of new members, the club treasurer suggests that for each new memb      Log On


   

Question 352873: there are currently 20 members in a school's ski club and the dues are $8 per member. to encourage the recruiting of new members, the club treasurer suggests that for each new member recruited, the dues for all members be reduced by 10 cents
a) how much membership money will the club have if it recruits 10 new members? 15 new memers? N new members?
b) for what value of N will be the club's total membership money be a maximum??
please help i am clueless in how to solve this problem thanks!!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the expression for membership money is ___ (members) * (dues) = money

where n is the number of new members ___ (20 + n)(8 - .1n) = m ___ 160 + 6n - .1n^2 = m

a) substitute the values for new members and solve for m

b) the maximum lies on the axis of symmetry of the quadratic
___ the general formula of the axis of symmetry for ax^2+bx+c is ___ x = -b / (2a)

in this case ___ n = -6 / [2(-.1)] ___ this is the number of new members for maximum money