Question

The Rocket Coaster has 16 cars, some that hold 6 people and some that hold 8 people. There is room for 106 people altogether. How many of each car are there on the Rocket Coaster?

Answer 1

The Rocket Coaster, having a combination of cars for 6 and 8 people and a total capacity of 106, has 11 cars that hold 6 people each and 5 cars that hold 8 people each.

Step-by-step explanation:

The Rocket Coaster has 16 cars with a combination of cars holding 6 people and cars holding 8 people. The total capacity of the coaster is 106 people. To find out the number of each type of car, we can set up two equations corresponding to the number of cars and the total number of people they can hold.

Let x represent the number of cars that hold 6 people, and y represent the number of cars that hold 8 people. We can write these equations:

1. x + y = 16 (The total number of cars)
2. 6x + 8y = 106 (The total capacity of people)

Now, we can solve this system of equations by using substitution or elimination. If we multiply the first equation by 6 and subtract it from the second equation, we get:

6x + 6y = 96 (after multiplying the first equation by 6)

6x + 8y = 106 (the original second equation)

Subtracting the first from the second, we get:

2y = 10

y = 5

Now that we know y, we can substitute it back into the first equation:

x + 5 = 16

x = 11

Therefore, there are 11 cars that hold 6 people and 5 cars that hold 8 people on the Rocket Coaster.