Question

There are currently 20 members in the school's Ski Club and the dues are $10 per member. To encourage the recruiting of new members, the club treasurer suggests that for each new member recruited, the dues for all members will be reduced by 10 cents. Write an equation in standard form to represent this situation.

Answer 1

`f(n)=-0.10n^2+8n+200`

Explanation:

Let n represent number of new members and f(n) represent membership money.

We have been given that there are currently 20 members in the school's Ski Club. So when n new members join, the total number of members would be
`20+n`.

Since for each new member recruited the dues for all members will be reduced by 10 cents, so new dues would be
`10-0.10n`.

The membership money would be number of total members times dues as:

`f(n)=(20+n)(10-0.10n)`

Since we need our equation in standard form, so we will use FOIL to expand our equation as:

`f(n)=20(10)-20(0.10n)+n(10)-n(0.10n)`

`f(n)=200-2n+10n-0.10n^2`

`f(n)=200+8n-0.10n^2`

`f(n)=-0.10n^2+8n+200`

Therefore, our required equation would be
`f(n)=-0.10n^2+8n+200`.