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 determine the original cost and the additional cost after the 10 students joined.
Let's assume the original cost of renting the bus was 'x' dollars.
When the cost was split evenly among the 20 students, each student paid x/20 dollars.
After 10 more students decided to go, we have a total of 30 students. So, when the cost was split evenly among the 30 students, each student paid (x + additional cost)/30 dollars.
According to the information given in the problem, dividing the cost among the 30 students brought the average cost down by $9.00 per person. This means:
(x + additional cost)/30 = (x/20) - 9
Now let's solve this equation to find the additional cost and, in turn, determine the total cost of renting the bus.
Multiply both sides of the equation by 30 to eliminate the denominators:
30 * [(x + additional cost)/30] = 30 * [(x/20) - 9]
Simplifying:
x + additional cost = 3x/2 - 270
Multiply both sides of the equation by 2 to eliminate the fraction:
2 * (x + additional cost) = 2 * (3x/2 - 270)
2x + 2 * additional cost = 3x - 540
Subtract 2x from both sides of the equation:
2 * additional cost = 3x - 2x - 540
2 * additional cost = x - 540
Simplifying further:
additional cost = x - 540
Now we know that the additional cost is equal to the original cost of renting the bus minus $540.
To find the original cost of renting the bus, we can solve the equation by substituting this value into the equation:
additional cost = x - 540
x - 540 = additional cost
Substituting this equation in the previous equation:
additional cost = x - 540
Therefore, the total cost of renting the bus is $540 plus the additional cost.
However, we do not have enough information to determine the value of x or the additional cost. The problem would require additional information or conditions to solve it accurately.