A30
B35
C40
D45
Answer:
A. 30
Read Explanation:
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.