Question

a patient is not allowed to have more than 270 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 135 milligrams of cholesterol. each ounce of meat provides 90 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 (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.
c. 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.
d. 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.

Explanation:

Step1: Set up inequality

Let $x$ be the number of eggs and $y$ be the number of ounces of meat. The inequality based on cholesterol - limit is $135x + 90y\leq270$.

Step2: Check option A

For the point $(1,4)$, substitute $x = 1$ and $y = 4$ into the inequality: $135\times1+90\times4=135 + 360=495>270$. So, option A is incorrect.

Step3: Check option B

For the point $(3,2)$, substitute $x = 3$ and $y = 2$ into the inequality: $135\times3+90\times2=405 + 180=585>270$. So, option B is incorrect.

Step4: Check option C

For the point $(1,1)$, substitute $x = 1$ and $y = 1$ into the inequality: $135\times1+90\times1=135 + 90=225\leq270$. So, option C is correct.

Step5: Check option D

For the point $(4,3)$, substitute $x = 4$ and $y = 3$ into the inequality: $135\times4+90\times3=540+270 = 810>270$. So, option D is incorrect.

Answer:

C. 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.