The senior class decided to have a picnic. A total of S seniors pledged to contribute equally for the $1000 fund. If 20 refused to honor their commitment, how much more would each of the rest of the seniors have to pay?

Printable View

- Dec 31st 2008, 08:25 AMSavior_Selfpretty simple abstract value problem
The senior class decided to have a picnic. A total of S seniors pledged to contribute equally for the $1000 fund. If 20 refused to honor their commitment, how much more would each of the rest of the seniors have to pay?

- Dec 31st 2008, 08:50 AMJD-Styles
If S seniors were going to split a $1000, then they were each going to pay 1000/S. Now, since 20 people aren't going to pay, everyone has to pay 1000/(S-20). The difference between the two amounts is:

$\displaystyle \frac{1000}{S-20}-\frac{1000}{S}$

Solve that and you'll have your answer. - Dec 31st 2008, 09:10 AMmasters
Your title says it's pretty simple. Why haven't you solved it then?

Let S = # seniors total

Let S - 20 = # seniors that actually contributed

Initially, each contributer promised to give $\displaystyle \frac{1000}{S}$

Later, after 20 reneged, it changed to $\displaystyle \frac{1000}{S-20}$

The amount extra that the S - 20 group had to give was:

$\displaystyle \frac{1000}{S-20}-\frac{1000}{S}=\frac{20000}{S(S-20)}$

Consider the following example:

Suppose S = 100

Initially, each would give 1000/100 = $10

Later, only 100 - 20 or 80 commited, so the new amount per senior = 1000/80 = $12.50.

The difference = $2.50 more.

Check it using the formula derived:

$\displaystyle \frac{20000}{S(S-20)}$$\displaystyle =\frac{20000}{100(100-20)}=\frac{20000}{8000} = \$2.50$

- Dec 31st 2008, 09:51 AMSavior_Self
Thanks guys. yeah, it's simple for you, but I haven't done these in a while, so I needed some confirmation.

Thanks again.