Question

If a and b are non-negative real numbers such that a+2b=6, then the average of the maximum and minimum possible values of (a+b) is

• A. 4
• B. 4.5
• C. 3.5
• D. 3

Answer 1

Answer: (B)

4.5

Answer 2

The correct answer is B: 4.5
Let's break down the problem step by step:
Given information: (a+2b=6)
We want to find the average of the maximum and minimum possible values of (a+b).
Step 1: Expressing (a) in terms of (b)
From (a+2b=6),we can solve for (a):
[a=6-2b]
Step 2: Finding Minimum and Maximum Values of (a+b)
Substitute the expression for (a) into (a+b):
[a+b=(6-2b)+b=6-b]
Since (a) and (b) are non-negative, the minimum value of (a+b) occurs when (b) is maximum [which is (b=3)],and the maximum value of (a+b) occurs when (b) is minimum [which is (b=0)].
Minimum value of (a+b):(6-3=3)
Maximum value of (a+b):(6-0=6)
Step 3: Finding Average
Average of maximum and minimum values:$\frac{3 + 6}{2}=\frac{9}{2}=4.5$
Therefore,the average of the maximum and minimum possible values of (a+b) is 4.5.