Question 544032
x is the number of ppl y is how much per person
number of ppl times amount of money per person = 400 bucks
{{{x*y=400}}} this is the given equation
{{{x=400/y}}}
two more ppl added to x and the amout y decreased by ten per person
{{{(x+2)*(y-10)=400}}} this is the given equation
{{{((400/y)+2)(y-10)=400}}} substitution for x
{{{400-(4000/y)+2y-20=400)}}} distribution
{{{400y-4000+2y^2-20y=400y}}}multiplied everything by y to get rid of y in denominator
{{{2y^2-20y-4000=0}}} added like terms
{{{2(y^2-10-2000)=0}}} simplified by taking out the two
{{{-50*40=-2000}}} found two numbers that multiply to get -2000 and add to get -10.
{{{2(y-50)(y+40)=0)}}} solve each equation for variable
{{{y=50}}}{{{y=-40}}} cant be negative
since we are talking about possitive numbers it has to be y=50
{{{x*y=400}}} take original equation
{{{x*50=400}}} insert y with 50
{{{x=400/50}}} solve for x
{{{x=8}}}
.
dont forget 2 people came last minute
{{{(x+2)*(y-10)=400}}} solve for x
{{{(8+2)*(50-10)=400}}}
{{{10*40=400}}}
{{{400=400}}} this confims that you are correct 
correct
{{{highlight(10)}}} people in limo at 40 bucks each