Question

If 48M+48N=2880, what is the average M and N?

• A. 30
• B. 35
• C. 40
• D. 45

Answer 1

Answer:

A. 30

Understanding the Concept of Average

• The average (also known as the mean) of a set of numbers is calculated by dividing the sum of those numbers by the count of the numbers.

• For two numbers, say M and N, the formula for their average is: Average = (M + N) / 2.

Step-by-Step Solution to the Problem

Identify the Given Equation

• You are given the equation: 48M + 48N = 2880.

Simplify the Equation through Factorization

• Notice that 48 is a common factor on the left side of the equation.

• Factor out 48: 48(M + N) = 2880.

• This step is crucial for simplifying the problem and is a common technique in algebraic equations.

Calculate the Sum of M and N

• To isolate (M + N), divide both sides of the equation by 48.

• (M + N) = 2880 / 48.

• Performing the division: 2880 ÷ 48 = 60.

• Thus, the sum of M and N is 60 (i.e., M + N = 60).

Compute the Average of M and N

• Now that we have the sum (M + N = 60), use the average formula for two numbers.

• Average = (M + N) / 2.

• Substitute the sum: Average = 60 / 2.

• The average of M and N is 30.