Answer:
Sure, I can help you with that!
To start, let's look at the ingredient list and see what information we have:
- 8 cups water
- ½ cup garlic
- ½ cup onion
- 1 ½ cups chopped carrots
- ½ cup tomato paste
- 2 cups sliced potatoes
- 1 cup olive oil
To make the calculations, we can set up ratios that relate the amount of each ingredient to the number of servings of soup. For example, if we want to know how much garlic we need for 40 servings of soup, we can set up the following ratio:
½ cup garlic / 10 servings = x cups garlic / 40 servings
To solve for x, we can cross-multiply and simplify:
(½ cup garlic) * 40 servings = (10 servings) * x cups garlic
20 cups = 10x
x = 2 cups
So we would need 2 cups of garlic to make 40 servings of soup.
Similarly, we can set up ratios for the other questions:
Question 2:
½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings
(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste
30 cups = 10x
x = 3 cups
So we would need 3 cups of tomato paste to make 60 servings of soup.
Question 3:
1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots
45 cups = 10x
x = 4.5 cups
So we would need 4.5 cups of chopped carrots to make 30 servings of soup.
here I simplified and checked the cross products of the ratios.
Question 1:
½ cup garlic / 10 servings = x cups garlic / 40 servings
Cross-multiplying, we get:
(½ cup garlic) * 40 servings = (10 servings) * x cups garlic
20 cups = 10x
Dividing both sides by 10, we get:
x = 2 cups garlic
Therefore, we need 2 cups of garlic to make 40 servings of soup.
Checking the cross products:
(½ cup garlic) * 40 servings = (10 servings) * 2 cups garlic
20 cups = 20 cups
The cross products are equal, so my answer is correct.
Question 2:
½ cup tomato paste / 10 servings = x cups tomato paste / 60 servings
Cross-multiplying, we get:
(½ cup tomato paste) * 60 servings = (10 servings) * x cups tomato paste
30 cups = 10x
Dividing both sides by 10, we get:
x = 3 cups tomato paste
Therefore, we need 3 cups of tomato paste to make 60 servings of soup.
Checking the cross products:
(½ cup tomato paste) * 60 servings = (10 servings) * 3 cups tomato paste
30 cups = 30 cups
The cross products are equal, so my answer is correct.
Question 3:
1 ½ cups chopped carrots / 10 servings = x cups chopped carrots / 30 servings
Cross-multiplying, we get:
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * x cups chopped carrots
45 cups = 10x
Dividing both sides by 10, we get:
x = 4.5 cups chopped carrots
Therefore, we need 4.5 cups of chopped carrots to make 30 servings of soup.
Checking the cross products:
(1 ½ cups chopped carrots) * 30 servings = (10 servings) * 4.5 cups chopped carrots
45 cups = 45 cups
The cross products are equal, so my answer is correct.