14.1k views
1 vote
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?

User TheFogger
by
7.1k points

2 Answers

4 votes

Answer:

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.

User Nickesha
by
7.9k points
4 votes
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.
User TheOne
by
9.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories