Han and Tyler are following a polenta that uses 5 cups of water for every 2 cups of cornmeal — Han says “I am using 3 cups of water. I will need 1 1/5 cups of cornmeal.”
— Tyler says, “ I am using 3 cups of cornmeal. I will need 7 1/2 cups of water.”

Both Han and Tyler were right.

Explanation:

Ratio is used to show relations between two units (size, number, length, amount etc.) It shows how many times is one value bigger/smaller than the other.

Here, we are given the ratio of water to cornmeal is 5:2.

Now, let's check their math.

Han claims he needs 3 cups of water and 1 1/5 cups of cornmeal. We want to set the proprtion to check whether Han's ratio matches with tthe given one:

5 : 2 = 3 : 1 1/5

We multiply outer values on one side and inner values on the other side:

5 • 1 1/5 = 3 • 2

6 = 6

We get the same value on both sides, which mens Han's math was correct.

Now for Tyler's. He says he needs 7 1/2 cups of water for 3 cups of cornmeal.

Let's write a proportion to see of it checks out to the given ratio:

5 : 2 = 7 1/2 : 3

Again we do the multiplication:

5 • 3 = 2 • 7 1/2

15 = 15

Again, the numbers match, so Tyler's math was also correct.