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

Question

3 years ago

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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 4 people and each large car can hold 7 people. The students rented twice as many large cars as small cars, which altogether can hold 72 people. Determine the number of small cars rented and the number of large cars rented.

Mathematics

1 answer:

maxonik [38] · Answer 1 · 2022-04-12T15:22:54+03:00

The students rented 4 small cars and 8 large cars.

Step-by-step explanation:

Given,

Number of people in small car = 4

Number of people in large car = 7

Total people in both type of cars = 72

Let,

x represent the number of small cars rented.

y represent the number of large cars rented.

According to given statement;

4x+7y=72 Eqn 1

y = 2x Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$4x+7(2x)=72\\4x+14x=72\\18x=72$

Dividing both sides by 18

$\frac{18x}{18}=\frac{72}{18}\\x=4$

Putting x=4 in Eqn 2

$y=2(4)\\y=8$

The students rented 4 small cars and 8 large cars.

Keywords: linear equation, substitution method

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