Question

The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1400, which was to be divided equally among the members going. Prior to the trip, 3 members decided not to go. If the cost per person increased by $105, how many people went on the expedition?

Answer 1

5 people

Explanation:

Let

• x = number of people

• y = cost per person

The total cost was $1400, which was to be divided equally among the members going. Then,

y = 1400 / x [1]

Prior to the trip, 3 members decided not to go. The cost per person increased by $105.

y + 105 = 1400 / (x - 3)

(y + 105) . (x - 3) = 1400 [2]

We replace [1] in [2],

(1400/x + 105) . (x - 3) = 1400

1400 - 4200/x + 105x -315 = 1400

- 4200/x + 105x = 315

(- 4200 + 105x²)/x = 315

- 4200 + 105x² = 315 x

105x² - 315x - 4200 = 0

When we solve this quadratic equation using the quadratic formula, we get x₁ = 8 and x₂ = -5. Only the positive x has sense.

The people that went to the expedition was x - 3 = 8 - 3 = 5.

Answer 2

To find the rate per person, we divide the additional $105 by the three people who backed out. The quotient would be 35. Hence, each person should pay $35. To determine how many people went to the expedition, divide the $1400 + $105 by 35, the answer is 43. Since 3 backed out, then the total number who actually went was 40.