Question

a patient is not allowed to have more than 562 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 104 milligrams of cholesterol. each ounce of meat provides 138 milligrams of cholesterol. completes parts (a) through (c) below.
c. select an ordered - pair satisfying the inequality. what are its coordinates and what do they represent in this situation? choose the correct answer below.
a. the point can be (1,4). the point (1,4) means that a patient had 1 egg and 4 ounces of meat during a day. this is within a diet of eggs and meat.
b. the point can be (1,1). the point (1,1) means that a patient had 1 egg and 1 ounce of meat during a day. this is within a diet of eggs and meat.
c. the point can be (4,3). the point (4,3) means that a patient had 4 eggs and 3 ounces of meat during a day. this is within a diet of eggs and meat.
d. the point can be (3,2). the point (3,2) means that a patient had 3 eggs and 2 ounces of meat during a day. this is within a diet of eggs and meat.

Explanation:

Step1: Set up the inequality

Let $x$ be the number of eggs and $y$ be the number of ounces of meat. The total cholesterol intake is $104x + 138y$, and the patient is not allowed more than 562 milligrams of cholesterol per day. So the inequality is $104x+138y\leq562$.

Step2: Check option A

For the point $(1,4)$, substitute $x = 1$ and $y = 4$ into the left - hand side of the inequality: $104\times1+138\times4=104 + 552=656>562$. So it does not satisfy the inequality.

Step3: Check option B

For the point $(1,1)$, substitute $x = 1$ and $y = 1$ into the left - hand side of the inequality: $104\times1+138\times1=104 + 138 = 242<562$. It satisfies the inequality.

Step4: Check option C

For the point $(4,3)$, substitute $x = 4$ and $y = 3$ into the left - hand side of the inequality: $104\times4+138\times3=416+414 = 830>562$. So it does not satisfy the inequality.

Step5: Check option D

For the point $(3,2)$, substitute $x = 3$ and $y = 2$ into the left - hand side of the inequality: $104\times3+138\times2=312 + 276=588>562$. So it does not satisfy the inequality.

Answer:

B. The point can be (1,1). The point (1,1) means that a patient had 1 egg and 1 ounce of meat during a day. This is within a diet of eggs and meat.