Question 1167719


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.