Question

A preschool has Campbell's Chunky Beef soup, which contains 2.5 g of fat and 15 mg of cholesterol per serving (cup), and Campbell's Chunky Sirloin Burger soup, which contains 7 g of fat and 15 mg of cholesterol per serving. By combining the soups, it is possible to get 12 servings of soup that will have 66 g of fat and 180 mg of cholesterol. How many cups of each soup should be used?

Answer 1

Answer:

4 cups of Campbell's Chunky Beef soup and 8 cups Campbell's Chunky Sirloin Burger soup should be used.

Step-by-step explanation:

Given:

Campbell's Chunky Beef soup contains 2.5 g of fat and 15 mg of cholesterol per serving (cup) and Chunky Sirloin Burger soup contains of fat 7g and cholesterol 15 mg.

And, 12 cup of soup having 66 g of fat and 180 mg of cholesterol is made by merging Chunky Beef soup and Chunky Sirloin soup.

Now, to find the cups of Campbell's Chunky Beef soup and cups of Campbell's Chunky Sirloin Burger soup that should be used.

Let the cups of Campbell's Chunky Beef soup be $x.$

Let the cups Campbell's Chunky Sirloin Burger soup be $y.$

So, total fats combining of both soup:

$2.5x+7y=66$ ........(1)

So, total cholesterol combining of both soup:

$15x+15y=180$

$15(x+y)=180$

Dividing both sides by 15 we get:

$x+y=12$

$y=12-x \ \ \ \ ........(2)$

Now, solving the equation (1):

$2.5x+7y=66$

Substituting the value of $y$ from equation (2) we get:

$2.5x+7(12-x)=66$

$2.5x+84-7x=66$

$84-4.5x=66$

Subtracting both sides by 84 we get:

$-4.5x=-18$

Dividing both sides by -4.5 we get:

$x=4.$

The cups of Campbell's Chunky Beef soup = 4.

Now, substituting the value of $x$ in equation (2):

$y=12-x\\\\y=12-4\\\\y=8.$

The cups Campbell's Chunky Sirloin Burger soup = 8.

Therefore, 4 cups of Campbell's Chunky Beef soup and 8 cups Campbell's Chunky Sirloin Burger soup should be used.