During 2005, a company produced an average of 2,000 products per month. How many products will the company need to...

1. Translate the problem requirements: Clarify what "increase monthly average by 200%" means (new average = \(3 \times \mathrm{old\ average}\)) and identify what we need to find (total production from 2006-2008)
2. Calculate the target monthly average: Determine what the new monthly average should be after the 200% increase
3. Find total production needed for the entire period: Calculate total production required from 2005-2008 to achieve the target average
4. Subtract known production to find the unknown: Remove 2005 production from total to find 2006-2008 production needed

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what this problem is asking in plain English. The company wants to increase its monthly average by 200%. This is a common source of confusion, so let's be very clear about what this means.

When we say "increase by 200%," we mean the new value will be the original value PLUS 200% of the original value. Think of it like this: if you had \$100 and someone increased it by 200%, you'd have your original \$100 plus an additional \$200 (which is 200% of \$100), giving you \$300 total.

So if the 2005 average was 2,000 products per month, then:

• Original average: 2,000 products/month
• Increase: \(200\% \times 2000 = 2 \times 2000 = 4000\) products/month
• New average: \(2000 + 4000 = 6000\) products/month

Or more simply: New average = \(2000 \times (1 + 2) = 2000 \times 3 = 6000\) products/month

We need to find: How many products must be produced from 2006 through 2008 to achieve this new average?

Process Skill: TRANSLATE - Converting the percentage increase language into concrete numbers

2. Calculate the target monthly average

From our translation above, we've determined that the target monthly average for the entire period 2005-2008 should be 6,000 products per month.

Let's verify this makes sense: If they averaged 2,000 per month in 2005, and we want the overall average to be 3 times higher, then 6,000 per month seems right.

3. Find total production needed for the entire period

Now we need to figure out the total production required for the entire period from 2005 through 2008.

First, let's count the months:

• 2005: 12 months
• 2006: 12 months
• 2007: 12 months
• 2008: 12 months
• Total: 48 months

If we want an average of 6,000 products per month over 48 months, then:
Total production needed = \(6000 \times 48 = 288000\) products

4. Subtract known production to find the unknown

We know what happened in 2005, so let's calculate that first:
2005 production = \(2000 \times 12 = 24000\) products

To find what we need from 2006-2008:
Production needed (2006-2008) = Total needed - 2005 production
Production needed (2006-2008) = \(288000 - 24000 = 264000\) products

5. Final Answer

The company needs to produce 264,000 products from 2006 through 2008.

Let's verify:

• 2005 production: 24,000
• 2006-2008 production: 264,000
• Total: 288,000 products over 48 months
• Average: \(288000 \div 48 = 6000\) products/month ✓
• This is indeed 3 times the original 2,000/month average ✓

The answer is (D) 264,000.

Common Faltering Points

Errors while devising the approach

Many students confuse "increase by 200%" with "increase to 200%" or think it means the new value becomes 200% of the original. The correct interpretation is that the new value = original + (200% of original) = original × 3. Students often calculate the new average as \(2000 \times 2 = 4000\) instead of \(2000 \times 3 = 6000\).

Students may incorrectly think they need to find the average for 2006-2008 only, rather than understanding that the 200% increase applies to the overall average for the entire period from 2005 through 2008. This leads to setting up the wrong equation structure.

Some students may try to calculate the total production for all years (2005-2008) instead of specifically what's needed for 2006-2008 only, which is what the question is asking for.

Errors while executing the approach

Students may make computational mistakes when calculating \(6000 \times 48 = 288000\) or when subtracting \(288000 - 24000 = 264000\). These straightforward arithmetic errors can lead to selecting incorrect answer choices.

Some students might miscalculate the total number of months in the period 2005-2008, perhaps counting it as 36 months (thinking 3 years × 12) instead of the correct 48 months (4 years × 12), leading to wrong total production calculations.

Errors while selecting the answer

No likely faltering points - once students have correctly calculated 264,000, the answer selection is straightforward as this value appears directly in choice (D).