Question

Han and Tyler are following a polenta recipe that uses 5 cups of water for every 2 cups of cornmeal.

- Han says, "I am using 3 cups of water, so I will need 1 1/2 cups of cornmeal."
- Tyler says, "I am using 3 cups of cornmeal, so I will need 7 1/2 cups of water."

Do you agree with either of them? Explain and show your reasoning. Use complete sentences.

Hint: 1/5 = 1/5 = 0.2
Hint: 7 1/2 = 15/2 = 7.5
Hint: How many cups of polenta do you need for 1 cup of water?

Answer 1

Han should use 1.2 cups of cornmeal, not 1.5, for 3 cups of water. Tyler is correct; he needs 7.5 cups of water for 3 cups of cornmeal.

Step-by-step explanation:

Let's first address Han's statement. The recipe calls for 5 cups of water for every 2 cups of cornmeal. To find out how much cornmeal Han needs for 3 cups of water, we set up a proportion:

​​(​​5 cups water / 2 cups cornmeal) = (3 cups water / x cups cornmeal)

​​Multiplying both sides of the equation by x and then by 2/5, we have:

x = (3 cups water) * (2 cups cornmeal) / (5 cups water)

x = (3 * 2) / 5

x = 6 / 5

x = 1.2 cups of cornmeal

So, Han should use 1.2 cups of cornmeal, not 1.5 cups as he initially thought.

Now let's look at Tyler's statement. To find out how much water Tyler needs for 3 cups of cornmeal, we use the same proportion:

(2 cups cornmeal / 5 cups water) = (3 cups cornmeal / y cups water)

​​Multiplying both sides of the equation by y and then by 5/2, we have:

y = (3 cups cornmeal) * (5 cups water) / (2 cups cornmeal)

y = (3 * 5) / 2

y = 15 / 2

y = 7.5 cups of water

Tyler is correct in stating he would need 7.5 cups of water for 3 cups of cornmeal.