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?
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?
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.
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$