# pretty simple abstract value problem

• Dec 31st 2008, 09:25 AM
Savior_Self
pretty 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, 09:50 AM JD-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:

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

• Dec 31st 2008, 10:10 AM
masters
Quote:

Originally Posted by Savior_Self
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? 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 $\frac{1000}{S}$ Later, after 20 reneged, it changed to $\frac{1000}{S-20}$ The amount extra that the S - 20 group had to give was: $\frac{1000}{S-20}-\frac{1000}{S}=\frac{20000}{S(S-20)}$ 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:

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

• Dec 31st 2008, 10:51 AM
Savior_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.