The cost of renting a bus to go snowboarding was split evenly by the 20 students planning to go. The day before the trip, 10 more students decided to go. Dividing the cost evenly among all 30 students brought the average cost down by $9.00 per person. What was the total cost of renting the bus?
To find the total cost of renting the bus, we need to work through the given information step by step.
Let's assume the original cost of renting the bus was x dollars.
Initially, there were 20 students planning to go, so each student would have paid x/20 dollars.
The day before the trip, 10 more students decided to go, making a total of 30 students.
Now, the cost needs to be divided evenly among all 30 students. We know that the average cost per person reduced by $9.00 after the additional students joined.
So, the new cost per person is (x/30) dollars, which is $9.00 less than the initial cost per person, (x/20) dollars.
We can set up an equation to represent this:
(x/20) - (x/30) = 9
To solve this equation, we need to find a common denominator:
(3x - 2x) / (60) = 9
Simplifying the equation further:
x / 60 = 9
Now, we can solve for x by multiplying both sides of the equation by 60:
x = 540
Therefore, the total cost of renting the bus was $540.