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 5 people and each large car can hold 7 people. The students rented 2 more small cars than large cars, which altogether can hold 46 people. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.

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Answer 1

Let's define the variables:

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

We can create a system of equations to represent the problem:

Equation 1: x + y = total number of cars rented
Equation 2: 7x + 5y = total number of people the cars can hold

We know from the problem that the number of small cars rented is 2 more than the number of large cars rented, so we can substitute y = x + 2 into Equation 1:

x + (x + 2) = total number of cars rented

Simplifying this equation gives:

2x + 2 = total number of cars rented

We also know from the problem that the cars rented can hold a total of 46 people, so we can substitute 46 for the total number of people the cars can hold in Equation 2:

7x + 5y = 46

Substituting y = x + 2 gives:

7x + 5(x + 2) = 46

Simplifying this equation gives:

12x + 10 = 46

Therefore, the system of equations that could be used to determine the number of small cars rented and the number of large cars rented is:

2x + 2 = total number of cars rented
7x + 5(x + 2) = 46