SOLUTION: A group of friends hire a bus for a day for $480. At the last minute, two more people decide to go on the trip, and as a result each person pays $8 less. How many people went on t

Question 1167719: A group of friends hire a bus for a day for $480. At the last minute, two more people decide to go on the
trip, and as a result each person pays $8 less. How many people went on the trip?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

the cost for the bus equals the number of people taking the bus times the amount that each person pays.

your equation is x * y = 480.

x is the number of people taking the bus and y is the amount that each person pays.

when you increase the number of people by 2 and reduce the price that each person pays by 8 dollars, then the formula becomes:

(x + 2) * (y - 8) = 480

in the first equation, solve for y to get y = 480 / x

in the second equation, replace y with 480 / x to get:

(x + 2) * (480 / x - 8) = 480

multiply both sides of this equation by x to get:

x * (x + 2) * (480 / x - 8) = 480 * x

simplify by multiplying x * (480/x - 8) to get:

(x + 2) * (480 - 8x) = 480 * x

simplify to get:

480 * x - 8x^2 + 960 - 16x = 480 * x

subtract 480 * x from both sides of the equation to get:

-8x^2 + 960 - 16x = 0

order by descending order of degree to get:

-8x^2 - 16x + 960 = 0

divide both sides of the equation by 8 to get:

-x^2 - 2x + 120 = 0

multiply both sides of the equation by -1 to get:

x^2 + 2x - 120 = 0

factor this quadratic to get:

(x + 12) * (x - 10) = 0

solve for x to get:

x = -12 or x = 10

x can't be negative, so x = 10

x * y = 10 * y = 480
solve for y to get:
y = 48

(x + 2) * (y - 8) = 480 becomes:
12 * 40 = 480
simplify to get:
480 = 480

this confirms the solution is correct.

your solution is that 12 people went on the trip.

if 10 went, the price was 480 / 10 = 48 for each person.
since 12 went, the price was 480 / 12 = 40 for each person.

each person paid 8 less.

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