Question 110213
You set up the problem correctly, except that I started with {{{px=825}}}
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The next step was to write: {{{(p+4)*(x-20)=825}}}
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Since {{{px}}} and {{{(p+4)*(x-20)}}} both equal the same thing, you can write:
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{{{px=(p+4)(x-20)}}}
:
{{{px=px+4x-20p-80}}}
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{{{4x-20p-80=0}}}, but we know that {{{x=825/p}}}, so:
:
{{{4(825/p)-20p-80=0}}},
{{{3300/p-20p-80=0}}}
{{{20p^2+80p-3300=0}}}
{{{p^2+4p-115=0}}}, which factors to:
{{{(p-11)(p+15)=0}}}
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Hence, {{{p=11}}} or {{{p=-15}}}.
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Throw out the negative result because you can't have a negative number of people on a team, and your answer is 11.
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Check:
{{{875/11=75}}}
{{{875/15=55}}}, 15 is 4 more than 11, and 55 is 20 less than 75.  Check.