Question

In a certain city, 20°F was the average (arithmetic mean) of the low temperatures of \(x^\circ\)F, 25°F, and 37°F on three consecutive days. 
 

Column A	Column B
\(x\)	0

Hint:

A useful trick for average problems is to think about the "sum deficit/surplus". The sum should be \(20 \times 3 = 60\). The known values are 25 (which is +5 from the average) and 37 (which is +17 from the average). The total surplus is \(5+17=22\). To balance this, \(x\) must be 22 below the average. \(20 - 22 = -2\).

Answer 1

Step 1: Understanding the Concept:
The problem requires finding a missing value from a set, given the average of the set.
Step 2: Key Formula or Approach:
The formula for the arithmetic mean (average) is:
\[ \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} \] We can rearrange this to find the sum: Sum of values = Average \( \times \) Number of values.
Step 3: Detailed Explanation:
We are given three temperatures: \(x\), 25, and 37.
The number of values is 3.
The average of these temperatures is 20.
Using the average formula:
\[ 20 = \frac{x + 25 + 37}{3} \] To solve for \(x\), first multiply both sides by 3:
\[ 20 \times 3 = x + 25 + 37 \] \[ 60 = x + 62 \] Now, subtract 62 from both sides to isolate \(x\):
\[ 60 - 62 = x \] \[ x = -2 \] So, the value for Column A is -2.
Step 4: Final Answer:
We are comparing Column A (\(x\)) and Column B (0).
Column A = -2
Column B = 0
Since \(-2<0\), the quantity in Column B is greater.