SOLUTION: A group of teenagers wanted to hire a small bus for their prom and they split the $600 total cost equally. If they had had 5 fewer people, each person would have paid $10 more. H

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Question 209245: A group of teenagers wanted to hire a small bus for their prom and they split the $600 total cost equally. If they had had 5 fewer people, each person would have paid $10 more. How many teenagers were there and how much did they each pay?
Found 2 solutions by scott8148, Theo:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let t = number of teens

"they split the $600 total cost equally" ___ 600 / t

" If they had had 5 fewer people, each person would have paid $10 more" ___ 600/(t - 5) = (600/t) + 10

multiplying by t(t-5) ___ 600t = 600t - 3000 + 10t^2 - 50t

subtracting 600t and dividing by 10 ___ 0 = t^2 - 5t - 300

factoring ___ 0 = (t + 15)(t - 20)

t + 15 = 0 ___ t = -15 ___ negative number not realistic

t - 20 = 0 ___ t = 20

substituting ___ $600 / 20 = $30

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = number of teenagers.
cost of the bus $600.00
let c = cost per teenager.
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formula to determine cost per teenager is c = $600/x
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if there were 5 less teenagers, the cost per teenager would have been $10 more.
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formula to determine cost per teenager when there is 5 less teenagers is:
c + 10 = $600 / (x-5)
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subtract 10 from this formula to get:
c = ( $600 / (x-5) ) - $10
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we have 2 formulas, each being equal to c so they are equal to each other.
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600 / x = ( 600 / (x-5) ) - 10
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multiply both sides of this equation by (x) * (x-5) to get:
600 * (x-5) = 600 * x - (10 * x * (x-5))
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this become:
( 600 * x ) - 3000 = ( 600 * x ) - ( 10 * x^2 ) + ( 50 * x )
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subtract everything on the right hand side of this equation from both sides of this equation to get:
(600*x) - 3000 - (600*x) + (10*x^2) - (50*x) = 0
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combine like terms to get:
10x^2 - 50x - 3000 = 0
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divide both sides of this equation by 10 to get:
x^2 - 5x - 300 = 0
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this factors out to be:
(x-20) * (x+15) = 0
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x = 20
or:
x = -15
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x has to be positive so the only possible solution is x = 20
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plug x = 20 into the original equations:
c = $600/x becomes c = $600/20 becomes c = $30.00
c+$10 = $600/(x-5) becomes c+$10 = $600/15 becomes c+$10 = $40 becomes c = $30.00
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your problem was:
A group of teenagers wanted to hire a small bus for their prom and they split the $600 total cost equally. If they had had 5 fewer people, each person would have paid $10 more. How many teenagers were there and how much did they each pay?
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answer is:
there were 20 teenagers there and the bus cost them $30.00 apiece.
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