A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1...

1. Translate the problem requirements: We need to find the arithmetic mean (average) annual salary. This means adding up all 6 employees' salaries and dividing by 6. We have: 2 employees at $14,000 each, 1 employee at $16,000, and 3 employees at $17,000 each.
2. Calculate total salary expenditure: Multiply each salary level by the number of employees earning that amount, then sum all salary payments.
3. Apply the average formula: Divide the total salary expenditure by the total number of employees (6) to find the average salary.
4. Match to closest answer choice: Compare the calculated average to the given options and select the closest value.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what we know in everyday terms. We have a bakery with 6 employees, and we want to find the average salary they pay. Think of this like finding the average height of students in a class - we add up all the heights and divide by the number of students.

Here's what each employee earns:

• 2 employees earn $14,000 each
• 1 employee earns $16,000
• 3 employees earn $17,000 each

To find the average (arithmetic mean), we need to add up all the money the bakery pays in salaries and divide by the total number of employees (6).

Process Skill: TRANSLATE - Converting the problem description into clear mathematical understanding

2. Calculate total salary expenditure

Now let's figure out how much the bakery spends on salaries in total. We'll multiply each salary amount by how many people earn that amount, then add everything together.

For the 2 employees earning $14,000 each:
\(2 \times \$14{,}000 = \$28{,}000\)

For the 1 employee earning $16,000:
\(1 \times \$16{,}000 = \$16{,}000\)

For the 3 employees earning $17,000 each:
\(3 \times \$17{,}000 = \$51{,}000\)

Total salary expenditure = \(\$28{,}000 + \$16{,}000 + \$51{,}000 = \$95{,}000\)

So the bakery pays out $95,000 total in annual salaries.

3. Apply the average formula

Now we can find the average salary. Remember, the average is just the total amount divided by the number of items (in this case, employees).

Average salary = Total salary expenditure ÷ Number of employees
Average salary = \(\$95{,}000 \div 6\)
Average salary = $15,833.33

4. Match to closest answer choice

Our calculated average is $15,833.33. Let's see which answer choice this is closest to:

1. $15,200 - This is $633.33 away from our answer
2. $15,500 - This is $333.33 away from our answer
3. $15,800 - This is only $33.33 away from our answer
4. $16,000 - This is $166.67 away from our answer
5. $16,400 - This is $566.67 away from our answer

Choice (C) $15,800 is closest to our calculated value of $15,833.33.

Final Answer

The average annual salary of the bakery employees is closest to $15,800. The answer is (C).

Common Faltering Points

Errors while devising the approach

Faltering Point 1: Misreading the employee distribution. Students may incorrectly interpret "each of the remaining 3 employees" and think there are only 3 employees total instead of 6. They might miss that 2 + 1 + 3 = 6 employees, leading them to use the wrong total when calculating the average.

Faltering Point 2: Confusing the average calculation method. Some students might try to find the average of the three salary amounts ($14,000, $16,000, $17,000) and divide by 3, forgetting that different numbers of employees earn each amount. This treats each salary level equally rather than weighting by the number of employees.

Errors while executing the approach

Faltering Point 1: Arithmetic errors in multiplication or addition. Students might make calculation mistakes when computing \(2 \times \$14{,}000 = \$28{,}000\), \(3 \times \$17{,}000 = \$51{,}000\), or when adding \(\$28{,}000 + \$16{,}000 + \$51{,}000 = \$95{,}000\). These errors compound and lead to an incorrect final average.

Faltering Point 2: Division errors when calculating the final average. When dividing \(\$95{,}000 \div 6\), students might make computational mistakes or stop at $15,833 without considering the decimal portion ($15,833.33), which affects which answer choice is closest.

Errors while selecting the answer

Faltering Point 1: Incorrectly determining which answer choice is "closest." Students might select the first answer choice they see that's reasonably close (like $16,000) without actually calculating the distance from their computed answer ($15,833.33) to each option. They need to find that $15,800 is only $33.33 away, making it the closest choice.