Question

Judy desires to increase both her protein consumption and caloric intake. She desires to have at least 72 more grams of protein each day and no more than an additional 480 calories daily. An ounce of parmesan cheese has 10 grams of protein and 30 calories. An ounce of cheddar cheese has 9 grams of protein and 120 calories.Write a system of 2 inequalities to model this situation. Use "x" for the ounces of parmesan cheese and "y" for the ounces of cheddar cheese.NOTE: You cannot have less than none!

Answer 1

30 x + 120y ≤ 480

10x + 9 y ≥ 72

Step-by-step explanation;

Here are Judy's requirements in a nutshell:

Additional Protein ≥ 72 grams

Additional Calories ≤ 480

Now, let us look at the protein and caloric value of Parmesan and Cheddar cheese.

For parmesan, 1 ounce has

10g protein

30 calories

Now if we have x ounces of parmesan, then the amounts they contain will be

10x grams protein

30x calories

For cheddar, 1 ounce has

9g protein

120 calories

Now if we have y ounces of cheddar, then the amounts they contain will be

9y grams protein

120y calories

Therefore, if I have x ounces of parmesan and y ounces of cheddar cheese, then Judy's protein requirement tells us that

`\boxed{10x+9y\ge72}`

and her caloric requirement tells us that

`\boxed{30x+120y\le480}`

Plotting these two inequalities gives