The rocket coaster has 15 cars, some hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6- passenger cars are there?

Answer 1

We have 2 unknowns, therefore we must have 2 equations to solve this.

Let x = # of 4-passenger cars

y = # of 6-passenger cars

Eq. I: x + y = 15

Eq. II 4x + 6y = 72

We can solve for either unknown by using the substitution or elimination methods. Let's use the elimination method to solve for y. First, multiply Eq. I by 4 to get 4x + 4y = 60. Now let's subtract this from Eq. II and solve for y:

4x + 6y = 72 Eq. II

-(4x + 4y = 60) subtracting Eq. I

0x + 2y = 12 difference

2y = 12 simplified

y = 12/2 divide both sides by 2 to isolate y

y = 6 solve for y

Substituting this value for y in Eq. I we can now solve for x:

x + y = 15 Eq. I

x + 6 = 15 substituting 6 for y

x = 15 - 6 subtract both sides to isolate x

x = 9 solve for x

By using these values for x and y in both equations for a check we can see that these answers are correct. So, there are 9 4-passenger cars and 6 6-passenger cars.

Hope this helps!