SOLUTION: several friends from big city high school decide to rent a limo for the prom for $400. at the last minute, 2 more people decided to join the group and this caused the cost per pers

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Question 544032: several friends from big city high school decide to rent a limo for the prom for $400. at the last minute, 2 more people decided to join the group and this caused the cost per person to decrease by $10. in all, how many people made the trip?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x is the number of ppl y is how much per person
number of ppl times amount of money per person = 400 bucks
x%2Ay=400 this is the given equation
x=400%2Fy
two more ppl added to x and the amout y decreased by ten per person
%28x%2B2%29%2A%28y-10%29=400 this is the given equation
%28%28400%2Fy%29%2B2%29%28y-10%29=400 substitution for x
400-%284000%2Fy%29%2B2y-20=400%29 distribution
400y-4000%2B2y%5E2-20y=400ymultiplied everything by y to get rid of y in denominator
2y%5E2-20y-4000=0 added like terms
2%28y%5E2-10-2000%29=0 simplified by taking out the two
-50%2A40=-2000 found two numbers that multiply to get -2000 and add to get -10.
2%28y-50%29%28y%2B40%29=0%29 solve each equation for variable
y=50y=-40 cant be negative
since we are talking about possitive numbers it has to be y=50
x%2Ay=400 take original equation
x%2A50=400 insert y with 50
x=400%2F50 solve for x
x=8
.
dont forget 2 people came last minute
%28x%2B2%29%2A%28y-10%29=400 solve for x
%288%2B2%29%2A%2850-10%29=400
10%2A40=400
400=400 this confims that you are correct
correct
highlight%2810%29 people in limo at 40 bucks each