The rocket coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is a room for 72 people altogether. How many 4 passenger cars are there? How many 6 passenger cars are there?
let the number of 4-people cars be x
then the number of 6-person cars is 15-x
4x + 6(15-x) = 72
4x + 90 - 6x = 72
-2x = -18
x = 9
9 of the 4-person cars and 6 of the 6-person cars
To find the number of 4 passenger cars and 6 passenger cars on the rocket coaster, let's set up a system of equations.
Let's assume x represents the number of 4 passenger cars, and y represents the number of 6 passenger cars.
From the given information, we know that there are a total of 15 cars. Therefore, we can write the equation:
x + y = 15
Also, we are told that the total number of people that can be accommodated in the cars is 72. So, using this information, we can set up another equation:
4x + 6y = 72
Now we have our system of equations:
x + y = 15
4x + 6y = 72
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method to solve it.
Multiply the first equation by 4 to eliminate the x variable:
4(x + y) = 4(15)
4x + 4y = 60
Now subtract the second equation from this new equation:
(4x + 4y) - (4x + 6y) = 60 - 72
-2y = -12
Divide both sides of the equation by -2:
y = (-12) / (-2)
y = 6
Substitute this value of y back into the first equation to find x:
x + 6 = 15
x = 15 - 6
x = 9
So, there are 9 four-passenger cars and 6 six-passenger cars on the rocket coaster.