Question

A group of college students are going to a lake house for the weekend and plan on renting small cars and

large cars to make the trip. Each small car can hold 4 people and each large car can hold 6 people. The
students rented 3 times as many small cars as large cars, which altogether can hold 36 people. Graphically
solve a system of equations in order to determine the number of small cars rented, x, and the number of
large cars rented, y.

Answer 1

To determine the number of small cars rented, x, and the number of large cars rented, y, we can set up a system of equations based on the given information. Solving this system of equations, we find that the students rented 6 small cars and 2 large cars.

Step-by-step explanation:

To solve this problem using a system of equations, we can set up two equations based on the given information.

Let x be the number of small cars rented and y be the number of large cars rented.

From the problem, we know that each small car can hold 4 people and each large car can hold 6 people. So, the total number of people that can be accommodated by the rented cars is 4x + 6y.

It is also given that the students rented 3 times as many small cars as large cars, and the total number of people that can be accommodated is 36. So, we can set up the following equations:

4x + 6y = 36 (equation 1)

x = 3y (equation 2)

To solve the system of equations, we can substitute equation 2 into equation 1:

4(3y) + 6y = 36

12y + 6y = 36

18y = 36

y = 2

Substituting the value of y back into equation 2, we can find x:

x = 3(2)

x = 6

Therefore, the students rented 6 small cars and 2 large cars.