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. The students rented 5 more small cars than large cars, which altogether can hold 51 people. Determine the number of small cars rented and the number of large cars rented.

Answer 1

Answer: The number of small cars rented = 7

The number of large cars rented=2

Step-by-step explanation:

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

As per given statements , we have the following system of equations:

$5x+8y=51--------(1)\\\\ x=y+5--------------(2)$

Substitute the value of x from (2) in (1), we get

$5(y+5)+8y=51$

$5(y)+5(5)+8y=51$    (Distributive property)

$5y+25+8y=51$

$13y=51-25$  (Subtract 25 on both both sides)

$13y=26$

$y=2$ (Divide both sides by 13)

Put value of y in (2) , we get $x=2+5 =7$

∴ The number of small cars rented = 7

The number of large cars rented=2

Answer 2

Answer:

They rented 7 small cars and 2 large cars.

Step-by-step explanation: