Final answer:
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.