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?
30 * 9 = ?
There has to be an initial step because first there was 20 students
Oops! Sorry -- I didn't read the word "by."
Please repost your question so a real math tutor can respond.
So what is the first step in figuring it out????
The first step in solving a word problem is always to organize the information you have, and put it into equations to solve.
Let c be the cost per student originally.
The cost of the bus has not changed, so the cost/student * the number of students has not changed:
20c = 30(c-9)
To solve this problem, we need to set up an equation based on the given information.
Let's assume that the initial cost of renting the bus is C dollars. Since the cost was split evenly among the 20 students, the average cost per person before the 10 additional students joined was C/20 dollars.
When the 10 more students decided to go, the total number of students became 30. Now, the average cost per person became (C/30) dollars.
According to the information given, dividing the cost evenly among all 30 students brought the average cost down by $9.00 per person. So, we can write the equation as:
(C/30) + 9 = C/20
Now, let's solve this equation to find the value of C, which represents the total cost of renting the bus.
Multiplying the equation by the common denominator of 20 and 30, which is 600, we get:
20(C/30) + 20(9) = 30(C/20)
Simplifying this equation gives us:
(20C/30) + 180 = (30C/20)
Multiplying both sides of the equation by 60 to eliminate the denominators, we have:
2(20C) + 60(180) = 3(30C)
40C + 10800 = 90C
Subtracting 40C from both sides of the equation, we get:
10800 = 90C - 40C
Simplifying further gives us:
10800 = 50C
Now, dividing both sides of the equation by 50, we find:
C = 10800/50
C = 216
Therefore, the total cost of renting the bus is $216.