quadratic

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lula lula
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quadratic

The Extreme Rock Climbing Club planned a climbing expedition.  The total cost was $2000, which was to be divided equally among the members going.  Prior to the trip, 5 members decided not to go.  If the cost per person increased by $20, how many people went on the expedition?
AlgebraHouse AlgebraHouse
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Re: quadratic

2000
------ = original price per person
   x

2000
------- = new price per person
 x - 5

2000              2000
------ + 20 =  ------   {original price per person plus 20 equals new price per person}
   x                 x - 5

Multiply entire equation by least common denominator, x(x - 5).

2000(x - 5) + 20x(x - 5) = 2000x   {multiplied by x(x - 5)}
2000x - 10,000 + 20x² - 100x = 2000x   {used distributive property}
20x² - 100x - 10,000 = 0   {subtracted 2000x from each side}
x = 25 or -20   {used quadratic formula}

Since x = 25,
20 went on the expedition

- Algebra House