Chapter 8.9, Problem 4C

To determine

To write and graph:

An inequality describing the possible amounts of orange juice and grapefruit juice you can drink to meet your daily requirement for vitamin C.

Answer to Problem 4C

Our required inequality would be $15x+12y\ge 60$ .

Explanation of Solution

Given:

It is recommended that you get at least 60 milligrams of vitamin C each day. One fluid ounce of orange juice contains about 15 milligrams of vitamin C, and one fluid ounce of grapefruit juice contains about 12 milligrams.

Calculation:

Let x represent fluid ounces of orange juice and y represent fluid ounces of grapefruit juice.

We have been given that one fluid ounce of orange juice contains about 15 milligrams of vitamin C, so xfluid ounce of orange juice will contain $15x$ milligrams of vitamin C.

We have been given that one fluid ounce of grapefruit juice contains about 12 milligrams of vitamin C, so y fluid ounce of grapefruit juice will contain $12y$ milligrams of vitamin C.

Since we need to get at least 60 milligrams of vitamin C each day, so total amount of vitamin C should be greater than or equal to 60. We can represent this information in an inequality as:

  $15x+12y\ge 60$

Therefore, the inequality $15x+12y\ge 60$ represents possible amounts of orange juice and grapefruit juice.

Since we have a greater than or equal to sign, so boundary line of our inequality will be a solid line. Upon graphing our given inequality, we will get our required graph as shown below:

  

We know that visual representation is more effective than theoretical representation. Therefore, agraph shows more clearly that a function is linear or not.