Question

There are many different ways to make popcorn, including the hot air popperand the hot oil popper. The air popper produces 14 cups of popcorn in 2.5 minutes.The oil popper produces 16 cups in 3.5 minutes. Is there a proportional relationshipbetween the quantity of popcorn and the time it takes to make it? Justify youranswer.

Answer 1

There is no proportional relationship between the quantity of popcorn and the time it takes to make it.

Step-by-step explanation:

Yes, there is a proportional relationship between the quantity of popcorn and the time it takes to make it. To determine the relationship, we can compare the rates at which the two poppers produce popcorn.

The air popper produces 14 cups of popcorn in 2.5 minutes, so the rate of production is 14 cups / 2.5 minutes = 5.6 cups/minute.

The oil popper produces 16 cups of popcorn in 3.5 minutes, so the rate of production is 16 cups / 3.5 minutes = 4.57 cups/minute.

Since the rates of production for both poppers are not constant, we can conclude that there is no proportional relationship between the quantity of popcorn and the time it takes to make it.

Answer 2

Ok, so

If there's a proportional relationship, there should be a ratio between the quantity of popcorn and the time it takes to make it.

So, we can write this as:

`\begin{gathered} (14)/(2.5)\questeq(16)/(3.5) \\ 5.6\\e4.571 \end{gathered}`

As there is not a ratio, there is not a proportional relationship.