Agroup 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.

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

Step-by-step 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.

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 :

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~