Question

When making lasagna, Mr. Harrison uses 1 pound of sausage for every 3/4 of a pound of mozzarella cheese. For a dinner party, Mr. Harrison wants to make an extra-large lasagna with 1 pound of mozzarella cheese. How many sausages will he need?

Answer 1

Mr. Harrison needs 1 and 1/3 pounds of sausage for his extra-large lasagna with 1 pound of mozzarella cheese.

Step-by-step explanation:

When making lasagna, Mr. Harrison uses 1 pound of sausage for every 3/4 of a pound of mozzarella cheese. If he wants to make lasagna with 1 pound of mozzarella cheese, we need to determine how many pounds of sausage he will need.

First, we set up a proportion to solve for the unknown quantity of sausage. If 3/4 pound of cheese corresponds to 1 pound of sausage, then 1 pound of cheese will correspond to x pounds of sausage. The proportion can be set up as follows:

((3/4) : 1 = 1 : x)

We cross-multiply to solve for x:

((3/4) times x = 1 times 1)

((3/4) times x = 1)

To find x, divide both sides by \((3/4)\) or multiply both sides by the reciprocal of \((3/4)\), which is \((4/3)\):

(x times (4/3) = 1 \times (4/3)

(x = 4/3)

So, Mr. Harrison will need 4/3 pounds, or approximately 1 and 1/3 pounds of sausage for his extra-large lasagna with 1 pound of mozzarella cheese.

Answer 2

Mr. Harrison will need 1 and 1/3 or 2 pounds of sausages to make lasagna with 1 pound of mozzarella cheese.

To answer the question, let's use the ratio given. Mr. Harrison uses 1 pound of sausage for every 3/4 pound of mozzarella cheese. This ratio can be shown as :

1 pound of sausage : 3/4 pound of mozzarella cheese

If we have 1 pound of mozzarella cheese, we want to find out how much sausage corresponds to this amount of cheese.

First, we can convert the ratio to a form that shows the amount of sausage per 1 pound of cheese. Since we want the cheese portion of the ratio to be 1, we can simply invert the cheese amount of the ratio given :

(1 pound of sausage) / (3/4 pound of mozzarella cheese)

Multiplying both sides of the ratio by the inverse of 3/4 (which is 4/3) gives :

(1 pound of sausage) * (4/3) = (3/4 pound of mozzarella cheese) * (4/3)

Simplifying the right side, (3/4) * (4/3) equals 1, which is the amount of mozzarella cheese we're interested in. Now let's focus on the left side :

(1 pound of sausage) * (4/3) = X pounds of sausage

We know that 4/3 is equivalent to 1.3333 (repeating), so :

1 * 1.3333 = 1.3333 pounds of sausage

In other words, for 1 pound of mozzarella cheese, Mr. Harrison will need 1.3333 pounds of sausage, which can also be expressed as 1 and 1/3 pounds of sausage or approximately 1.33 pounds of sausage when rounded to two decimal places.

Since, it's not practical to have a fraction of a sausage, Mr. Harrison will need 2 pound sausages.