In Country C, the unemployment rate among construction workers dropped from 16% on September 1, 1992, to 9% on September...

1. Translate the problem requirements: We need to find the percent change in the actual number of unemployed construction workers (not the unemployment rate) between 1992 and 1996, given changes in both the unemployment rate and total workforce size.
2. Establish baseline numbers: Choose a convenient starting number for total construction workers in 1992 to make calculations simple and track both employed and unemployed workers.
3. Calculate 1996 workforce composition: Apply the 20% workforce growth and new 9% unemployment rate to determine the new number of unemployed workers.
4. Compare unemployment figures: Calculate the percent change between the actual number of unemployed workers in 1992 versus 1996 to find our answer.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what this problem is really asking. We have construction workers in Country C, and we're looking at two different time periods: September 1992 and September 1996.

The key point here is that we need to find the change in the actual number of unemployed workers, not the unemployment rate. The unemployment rate tells us what percentage of workers are unemployed, but the actual number depends on both the rate AND the total size of the workforce.

Here's what we know:
• 1992: 16% unemployment rate
• 1996: 9% unemployment rate
• 1996: 20% more total construction workers than in 1992

We need to figure out: Did the actual number of unemployed people go up or down, and by how much?

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

2. Establish baseline numbers

To make this concrete and easy to follow, let's pick a nice round number for the total construction workers in 1992. I'll use 100 workers - this makes the percentages easy to work with.

So in 1992:
• Total construction workers = 100
• Unemployment rate = 16%
• Number of unemployed workers = \(\mathrm{16\% \, of \, 100 = 16}\) people
• Number of employed workers = \(\mathrm{100 - 16 = 84}\) people

This gives us our starting point. Now we can see exactly how many unemployed people we had in 1992: 16 workers.

3. Calculate 1996 workforce composition

Now let's figure out what happened by 1996.

First, the total workforce grew by 20%:
• 1996 total workers = \(\mathrm{100 + (20\% \, of \, 100) = 100 + 20 = 120}\) workers

Next, we apply the new unemployment rate of 9%:
• 1996 unemployed workers = \(\mathrm{9\% \, of \, 120 = 0.09 \times 120 = 10.8}\) workers

So by 1996, we have about 10.8 unemployed construction workers compared to 16 unemployed workers in 1992.

4. Compare unemployment figures

Now we can compare the actual number of unemployed workers between the two years:

• 1992: 16 unemployed workers
• 1996: 10.8 unemployed workers

The change is: \(\mathrm{10.8 - 16 = -5.2}\) workers (a decrease)

To find the percent change:
Percent change = (New value - Old value) ÷ Old value × 100%
Percent change = \(\mathrm{(10.8 - 16) \div 16 \times 100\%}\)
Percent change = \(\mathrm{(-5.2) \div 16 \times 100\%}\)
Percent change = \(\mathrm{-0.325 \times 100\% = -32.5\%}\)

This is approximately a 30% decrease.

Process Skill: SIMPLIFY - Using round numbers (100 workers initially) made all calculations straightforward

Final Answer

The number of unemployed construction workers decreased by approximately 30% from 1992 to 1996.

Even though the total workforce grew by 20%, the unemployment rate dropped significantly (from 16% to 9%), resulting in fewer total unemployed workers.

The answer is (B) 30% decrease.

Common Faltering Points

Errors while devising the approach

1. Confusing unemployment rate change with actual number change

Students often see that the unemployment rate dropped from 16% to 9% and immediately think this means fewer unemployed people. They might calculate the rate change (16% to 9% = 7 percentage point decrease) without considering that the total workforce size also changed. This leads them to miss the key insight that we need to account for both the rate change AND the workforce growth.

2. Misunderstanding what "20% greater workforce" means

Students may incorrectly interpret "20% greater on September 1, 1996" as meaning the 1992 workforce was 20% of the 1996 workforce, rather than understanding that the 1996 workforce is 120% of the 1992 workforce (or 1.2 times larger).

3. Setting up the wrong comparison

Some students might try to compare employed workers instead of unemployed workers, or calculate the change in employment rate rather than focusing on the actual number of unemployed individuals that the question asks for.

Errors while executing the approach

1. Arithmetic errors in percentage calculations

When calculating 9% of 120, students might make basic multiplication errors (like getting 9.8 instead of 10.8) or forget to convert percentages to decimals properly (using 9 instead of 0.09).

2. Incorrect percent change formula application

Students often struggle with the percent change formula. They might use (10.8 - 16)/10.8 instead of (10.8 - 16)/16, forgetting that the denominator should be the original value (1992 figure), not the new value (1996 figure).

3. Sign confusion in the final calculation

When getting -5.2/-16 = -0.325, students might lose track of the negative sign or incorrectly conclude this represents an increase rather than a decrease.

Errors while selecting the answer

1. Rounding errors leading to wrong answer choice

Students who correctly calculate -32.5% might round this to -35% and look for that option, or might round to -32% and choose 30% simply because it's closest, without recognizing that -32.5% should indeed round to 30% decrease.

2. Selecting increase instead of decrease

Even after calculating the correct magnitude (~30%), students might select "(D) 30% increase" instead of "(B) 30% decrease" due to confusion about the direction of change or misreading their own negative result.

Alternate Solutions

Smart Numbers Approach

This problem is perfect for the smart numbers technique because we need to track changes in both workforce size and unemployment rates simultaneously. We can choose a convenient starting number that makes our calculations clean.

Step 1: Choose Smart Starting Number

Let's use 1,000 construction workers in 1992 as our baseline. This number is chosen because:

• It's easy to calculate percentages with
• It will give us whole numbers when we apply the given rates
• It makes the 20% increase calculation straightforward

Step 2: Calculate 1992 Unemployment

In 1992:

• Total construction workers = 1,000
• Unemployment rate = 16%
• Number of unemployed workers = \(\mathrm{16\% \times 1,000 = 160}\) unemployed workers

Step 3: Calculate 1996 Workforce Size

In 1996, the workforce was 20% larger:

• Total construction workers = \(\mathrm{1,000 + (20\% \times 1,000) = 1,000 + 200 = 1,200}\) workers

Step 4: Calculate 1996 Unemployment

In 1996:

• Total construction workers = 1,200
• Unemployment rate = 9%
• Number of unemployed workers = \(\mathrm{9\% \times 1,200 = 108}\) unemployed workers

Step 5: Calculate Percent Change in Unemployed Workers

Change in unemployed workers:

• 1992: 160 unemployed
• 1996: 108 unemployed
• Change = \(\mathrm{108 - 160 = -52}\) workers

Percent change = (Change ÷ Original) × 100%

Percent change = \(\mathrm{(-52 \div 160) \times 100\% = -0.325 \times 100\% = -32.5\%}\)

Step 6: Select Closest Answer

A 32.5% decrease is closest to 30% decrease.

Answer: (B) 30% decrease

Note: The beauty of smart numbers here is that any starting number would give us the same percentage result, but 1,000 made our calculations particularly clean and easy to follow.