A group of 45 people decide to rent a bus for a trip. They divide the cost equally. When five of the people decide not to go on the trip the rest of the people pay $10 more each.
How much does the bus cost?
$X/45 = Cost per person.
X/40 = X/45 + 10.
X/40 - X/45 = 10
0.025x - 0.0222x = 10
X = $3,600 = Cost of the bus.
Let's solve this step by step:
Step 1: Divide the total cost equally among the 45 people who originally planned to go on the trip.
Let's assume the initial cost per person is X.
Step 2: Multiply the initial cost per person (X) by the number of people (45) to find the total initial cost.
Total initial cost = X * 45
Step 3: After five people decide not to go, the remaining number of people is 45 - 5 = 40.
Step 4: When the remaining people divide the cost equally, they each pay $10 more than the initial cost per person (X).
So, the new cost per person is X + $10.
Step 5: Multiply the new cost per person (X + $10) by the number of remaining people (40) to find the new total cost.
New total cost = (X + $10) * 40
Since the total initial cost (Step 2) and the new total cost (Step 5) are the same, we can set up the equation:
X * 45 = (X + $10) * 40
Let's solve for X:
45X = 40X + 400
45X - 40X = 400
5X = 400
X = 400/5
X = $80
Therefore, the initial cost per person (and the cost of the bus) is $80.
To find out how much the bus costs, let's break down the information given in the problem:
1. Initially, there were 45 people who decided to rent a bus for a trip.
2. The cost of the bus was divided equally among the 45 people.
3. When 5 people decided not to go on the trip, the rest of the people had to pay $10 more each.
We need to determine the original cost of the bus. Let's follow these steps:
1. Initially, the cost per person can be represented by the equation: x dollars/person, where x is the total cost of the bus.
2. Since the cost was divided equally among the 45 people, the total cost of the bus can be found by multiplying the cost per person (x) by the number of people (45).
- Total cost of the bus = x * 45 = 45x dollars.
Now, let's consider the situation after 5 people decided not to go on the trip:
3. When those 5 people decided not to go, the remaining number of people on the trip would be 45 - 5 = 40 people.
4. As stated in the problem, the rest of the people (40 people) had to pay $10 more each.
- Total cost increase due to those 5 people not going = $10 * 40 = $400.
- Since the cost increase was distributed among the remaining 40 people, the new cost per person can be represented by (x + $10) dollars/person.
Now, we can set up an equation using the obtained information:
Original total cost of the bus = New total cost of the bus
45x dollars = 40(x + $10) dollars
Let's solve this equation to find the value of x, which represents the original cost of the bus.
45x = 40x + 400
45x - 40x = 400
5x = 400
x = 400 / 5
x = 80
Therefore, the original cost of the bus is $80.