Rock climbing expedition

The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1800, which was to be divided equally among the members going. Prior to the trip, 10 members decided not to go. If the cost per person increased by $90. How many people went on the expedition?

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x = number of members initially planning on going

1800/x = original cost per person
1800/(x - 10) = new cost per person

1800/x - 1800/(x - 10) = 90 {original cost per person minus new cost per person equals 90}
​1800(x - 10) - 1800x = 90x(x - 10) {multiplied entire equation by the least common denominator, x(x - 10)}
1800x - 18,000 - 1800x = 90x² - 900x {used distributive property}
-18,000 = 90x² - 900x {combined like terms on left and used distributive property on right}
90x² - 900x + 18,000 = 0 {added 18,000 to each side}
90(x² - 10x + 200) = 0 {factored 90 out}
x² - 10x + 200 = 0 {divided each side by 90}
(x - 20)(x + 10) = 0 {factored into two binomials}
x - 20 = 0 or x + 10 = 0 {set each factor equal to zero}
x = 20 or x = -10 {solved each equation}

​x = 20 originally planning to go {x cannot be negative}
​so, 10 people actually went

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