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 2 more large cars than
small cars, which altogether can hold 72 people. Graphically solve a system of
equations in order to determine the number of small cars rented, z, and the number
of large cars rented, y.

Answer 1

By solving a system of linear equations, it is determined that the students rented 6 small cars and 8 large cars for their trip to the lake house.

Step-by-step explanation:

To determine the number of small cars (z) and large cars (y) rented by a group of college students, we need to solve a system of linear equations. Based on the question, we have two key pieces of information:

• Each small car holds 4 people, and each large car holds 6 people.
• The students rented 2 more large cars than small cars, and altogether the cars can hold 72 people.

We can translate this information into two equations:

1. 4z + 6y = 72 (The total capacity of all cars combined can hold 72 people.)
2. y = z + 2 (There are 2 more large cars than small cars.)

To graphically solve this system, we would plot each equation as a line on a graph. The point where they intersect represents the solution. However, in this case, we can also solve the system algebraically:

1. Substitute y from the second equation into the first: 4z + 6(z + 2) = 72
2. Solve for z: 4z + 6z + 12 = 72 then 10z + 12 = 72, so 10z = 60 and z = 6.
3. Substitute z back into the second equation to find y: y = 6 + 2, so y = 8.

Therefore, the students rented 6 small cars and 8 large cars.