Question

1. read the word problem.

if meg is three times as old as her sister emily, and their total age is 16, how old is emily?

which logical variables can be used to represent the unknown of megs age in the word problem? select all that apply.

\\(a\\) = emilys age

\\(a\\) = megs age

\\(m\\) = megs age

\\(\pi\\) = megs age

Explanation:

⚡ Using what you learned: understanding linear equations

Step 1: Analyze the requirements for logical variables

A logical variable is a symbol used to represent an unknown value in a word problem. To be considered "logical" or practical for representing Meg's age:

• The variable should represent the correct unknown quantity specified by the question (Meg's age).
• The variable symbol itself should ideally be intuitive (such as \( m \) for Meg or a standard algebraic variable like \( a \)).
• Mathematical constants with fixed, universally defined values (like \( \pi \approx 3.14159 \)) should not be used as variables.

Step 2: Evaluate each option

1. \( a = \text{Emily's age} \): This represents Emily's age, not Meg's age. (Incorrect)
2. \( a = \text{Meg's age} \): Using a standard algebraic variable like \( a \) to represent Meg's age is logical and common in algebra. (Correct)
3. \( m = \text{Meg's age} \): Using the letter \( m \) (the first letter of Meg's name) is highly intuitive and logical. (Correct)
4. \( \pi = \text{Meg's age} \): The symbol \( \pi \) is a reserved mathematical constant representing the ratio of a circle's circumference to its diameter. It is not logical to use it as a variable. (Incorrect)

Answer:

• \( a = \text{Meg's age} \)
• \( m = \text{Meg's age} \)