Respuesta :
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.
Answer:
5 people
Step-by-step 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.