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.

Answer 1

3 large cars and 2 small cars

Explanation:

Let x = the number of small cars and

y = the number of large cars..

So 5 times the number of small cars plus 8 times the number of large cars would equal the number of students total in both cars.

That would be shown as 5x + 8y = 34.

The total number of cars is 5 which would be x + y = 5.

Start by finding the value of x in terms of y: x = 5-y

Then substitute the value if x by 5-y in the original formula.

5x + 8y = 34

5(5-y) + 8y = 34

Simplify the equation:

25 - 5y + 8y = 34

Solve for y:

3y = 34 - 25

3y = 9

y = 3

And solve for x by substituting

x + 3 = 5 in the value for y in the equation x + y = 5.

x + 3 = 5

x = 2.

So there are 3 large cars and 2 small cars.