Algebra 1 Word Problem

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 8 people. A total of 5 cars were rented which can hold 34 people altogether. Determine the number of small cars rented and the number of large cars rented.

Answer 1

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 sustituting 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.

Answer 2

5S + 8L = 34

S+L = 5

5S + 5L = 25

subtract last equation from the 1st

3L = 9

L = 3 large cars

S = 2 small cars