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 3 times as many small cars as large cars, which altogether can hold 44 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.

Answer 1

Answer with explanation:

We define variable as

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

Since ,

Each small car can hold 5 people and each large car can hold 7 people.

i.e. Number of people in x cars = 5x

Number of people in y cars = 7y

The students rented 3 times as many small cars as large cars, implies

y=3(x)

They altogether can hold 44 people.

i.e. 5x+7y=44

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

`y=3(x)`

`5x+7y=44`

Answer 2

The equation 7 m + 15 m = 44 is the equation that can be used to determine the number of small cars rented and the number of large cars rented.

where, m : Number of large cars rented

Explanation:

The number of people small car can hold = 5

The number of people large car can hold = 7

Let us assume the number of large cars rented = m

So, the number of smaller cars rented = 3 x ( Number of large cars rented)

= 3 m

Now, the number of people in m large cars = m x ( Capacity of 1 large car)

= m x ( 7) = 7 m

And, the number of people in 3 m small cars = 3 m x ( Capacity of 1 small car) = 3 m x ( 5) = 15 m

Total people altogether going for the plan = 44

⇒ The number of people in ( Small +Large) car = 44

or, 7 m + 15 m = 44

Hence, the equation 7 m + 15 m = 44 is the equation that can be used to determine the number of small cars rented and the number of large cars rented.