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Math Help - pretty simple abstract value problem

  1. #1
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    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?
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  2. #2
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    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}

    Solve that and you'll have your answer.
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  3. #3
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    Quote Originally Posted by Savior_Self View Post
    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


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  4. #4
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    Thanks guys. yeah, it's simple for you, but I haven't done these in a while, so I needed some confirmation.

    Thanks again.
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