Question 344366
Where's the 4 come from??
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Assume there are X people going originally.
Then the cost per person is 
{{{C[1]=575/X}}}
When you add the 2 people you now have X+2 people and the cost per person becomes,
{{{C[2]=575/(X+2)}}}
And you know that,
{{{C[2]=C[1]-2}}}
Now substitute into this equation.
{{{575/(X+2)=575/X-2}}}
Multiply both sides by the product of the denominators {{{X(X+2)}}}
{{{575X=575(X+2)-2X(X+2)}}}
{{{575X=575X+1150-2X^2-4X}}}
{{{2X^2+4X-1150=0}}}
{{{X^2+2X-575=0}}}
This equation is factorable.
{{{(X-23)(X+25)=0}}}
Two solutions but only the positive solution makes sense here.
{{{X-23=0}}}
{{{X=23}}}
When {{{X=23}}}, {{{C=575/23=25}}}dollars per person
When {{{X=25}}}, {{{C=575/25=23}}}dollars per person, a $2 reduction.