Question

Healthy Grocer is offering a special on cases of water bottles, but customers can buy no more than 10 cases at the sale price. The number of water bottles a customer receives is directly proportional to the number of cases purchased. A customer buying 5 cases gets 120 water bottles.

Write a direct variation to represent this situation. Use y to represent the number of water bottles and x to represent the number of cases.

Answer 1

y = 24x

Explanation:

In a direct variation, we have

output = k * input, with k being a positive number.

Therefore, with the output being the number of water bottles and the input being the number of cases, we have y = kx. We know that the output is y and the input is x because the question states that the number of water bottles (y) is directly proportional to the number of cases (x), so x must be multiplied by something to obtain y.

We have 120 water bottles as one output and 5 cases as its corresponding input.

120 = k(5)

divide both sides by 5 to isolate k

k = 24

y = 24x