A social club charters a bus at a cost of $560 to take a group of members on an excursion to Atlantic City. At the last minute, five people in the group decide not to go. This raises the transportation cost per person by $2. How many people originally intended to take the trip?

40 persons

Explanation:

Given:

Total cost of trip = $560

Number of people Decide not to go = 5 people

raise cost = $2

Assume:

Number of people wants to go = a

Cost per person = b

So, a x b = $560, b = 560/a

After people decided not to go,

Total number of people = (a-5)

New cost = (b+2)

So, total cost = (a-5) (b+2) = $560

ab + 2a - 5b - 10 = 560, where ab = $560

2a - 5b = 10

2a - 5b = 10

By putthing value of b

2a - 5 (560/a) = 10

2a - (2800 / a) = 10

2a² - 2800 = 10a

2a² - 10a - 2800 = 0

a = 40

Total 40 persons wants to go.