Question

this question has two parts. first, answer part a. then, answer part b
part a
linda has two cats. the difference in weight of her maine coon and siberian is at least 6 pounds. linda’s siberian has a weight of $8\frac{3}{4}$ pounds. choose the inequality that represents the possible weight of the maine coon.
a) $x - 8\frac{3}{4} \geq 6$
b) $x - 8\frac{3}{4} < 6$
c) $x - 6 \leq 8\frac{3}{4}$
d) $x - 6 > 8\frac{3}{4}$
part b
determine the possible weight of the maine coon. choose the correct answer and explanation

Explanation:

Part A

Step1: Define variables

Let \( x \) be the weight of the Maine Coon. The weight of the Siberian is \( 8\frac{3}{4} \) pounds. The difference in their weights is \( x - 8\frac{3}{4} \) (assuming \( x\geq8\frac{3}{4} \), if not, it would be \( 8\frac{3}{4}-x \), but since the inequality is about the difference being at least 6, and we want to represent the possible weight of the Maine Coon, we consider \( x - 8\frac{3}{4} \geq 6 \) because if the Maine Coon is heavier, the difference \( x - 8\frac{3}{4} \) is at least 6.

Step2: Match with options

Looking at the options, option A is \( x - 8\frac{3}{4} \geq 6 \), which matches our derived inequality.

Step1: Add \( 8\frac{3}{4} \) to both sides

To solve for \( x \), we add \( 8\frac{3}{4} \) to both sides of the inequality \( x - 8\frac{3}{4} \geq 6 \).
\( x - 8\frac{3}{4}+ 8\frac{3}{4}\geq 6 + 8\frac{3}{4} \)

Step2: Calculate the right - hand side

Convert 6 to a fraction with denominator 4: \( 6=\frac{24}{4} \), and \( 8\frac{3}{4}=\frac{35}{4} \). Then \( 6 + 8\frac{3}{4}=\frac{24}{4}+\frac{35}{4}=\frac{24 + 35}{4}=\frac{59}{4}=14\frac{3}{4} \). So \( x\geq14\frac{3}{4} \). The possible weight of the Maine Coon is at least \( 14\frac{3}{4} \) pounds. (Since the problem didn't provide all the options for Part B clearly, but if we follow the inequality from Part A, the solution is \( x\geq14\frac{3}{4} \))

Answer:

A. \( x - 8\frac{3}{4} \geq 6 \)

Part B (assuming we need to solve the inequality from Part A to find possible weight, but since the problem says "determine the possible weight of the Maine Coon", we can solve \( x - 8\frac{3}{4} \geq 6 \))