What algebraic expression represents the difference of two numbers if their sum is 32 and their difference is 12?

• A. p - q = 12
• B. p + q = 12
• C. p + q = 32
• D. p - q = 32

Answer: (A)

To understand why the appropriate expression to represent the difference of two numbers, given that their sum is 32 and their difference is 12, is correct, let's break down the information provided.

First, we have two numbers, which we can denote as ( p ) and ( q ). The problem states that their sum is 32, expressed as ( p + q = 32 ). Next, it states that their difference is 12, which is mathematically expressed as ( p - q = 12 ).

The expression representing the difference of these two numbers, ( p - q ), reflects the relationship between the two quantities, indicating how much larger one number is than the other. Since we have already established that this difference is given as 12, using the equation ( p - q = 12 ) perfectly encapsulates the condition provided in the question.

Thus, the expression accurately and directly corresponds to what the question is asking about the difference of the two numbers, making it the correct choice.

In contrast, statements about the sum would not align with the request for an expression focusing solely on the difference. The clear distinction is essential for accurately addressing mathematical relationships.