Question

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 4 times as many large cars as small cars, which altogether can hold 56 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. let x = the number of small cars rented let y = the number of large cars rented system of equations: answer attempt 1 out of 2

Explanation:

Step1: Define variables

Let \( x \) be the number of small cars rented, and \( y \) be the number of large cars rented.

Step2: Set up first equation (car relationship)

The number of large cars is 4 times the number of small cars, so \( y = 4x \).

Step3: Set up second equation (people capacity)

Each small car holds 4 people, so small cars hold \( 4x \) people. Each large car holds 6 people, so large cars hold \( 6y \) people. Total people is 56, so \( 4x + 6y = 56 \).

System of Equations:

\( y = 4x \)

\( 4x + 6y = 56 \)

(To solve, substitute \( y = 4x \) into the second equation: \( 4x + 6(4x) = 56 \), \( 4x + 24x = 56 \), \( 28x = 56 \), \( x = 2 \), then \( y = 4(2) = 8 \). But the question only asks for the system.)

Answer:

The system of equations is \(

$$\begin{cases} y = 4x \\ 4x + 6y = 56 \end{cases}$$

\)