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.

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