A bus tour company charges a flat fee for renting out the bus, and an additional amount for each person. If the price is quoted at $382 for 12 people and $430 for 16 people, what is the flat fee?
(430 - 382)/4 = 12 per person
12 * 12 = 144
382 - 144 = _$_____ flat fee
To find the flat fee charged by the bus tour company, we can first calculate the additional amount for each person.
Let's assume the additional amount for each person is 'x'.
For 12 people, the total cost would be the flat fee plus the product of the additional amount and the number of people:
Total cost for 12 people = Flat fee + x * 12 = $382
Similarly, for 16 people, the total cost would be the flat fee plus the product of the additional amount and the number of people:
Total cost for 16 people = Flat fee + x * 16 = $430
We can set up a system of two equations using these two situations:
Flat fee + x * 12 = $382 ---(Equation 1)
Flat fee + x * 16 = $430 ---(Equation 2)
Using these equations, we can solve for the flat fee.
To do that, we can subtract Equation 1 from Equation 2:
(Flat fee + x * 16) - (Flat fee + x * 12) = $430 - $382
This simplifies to:
x * 16 - x * 12 = $48
Simplifying further:
4x = $48
Dividing both sides by 4:
x = $12
Now that we have found the additional amount per person 'x' ($12), we can substitute it into Equation 1 to find the flat fee:
Flat fee + 12 * 12 = $382
Flat fee + 144 = $382
Subtracting 144 from both sides:
Flat fee = $382 - $144
Flat fee = $238
Therefore, the flat fee charged by the bus tour company is $238.