Let's solve the problem step-by-step: ### **Step 1: Assign Variables** Let the number of construction workers on September 1, 1992, be \( x \). ### **Step 2: Calculate the Number of Workers in 1996** On September 1, 1996, the number of construction workers is 20% greater than in 1992: \[ \text{Number of workers in 1996} = x + .2x = 1.2x \] ### **Step 3: Calculate the Number of Unemployed Workers in Each Year** #### **1992:** Unemployment rate = 16% \[ \text{Unemployed in 1992} = .16x \] #### **1996:** Unemployment rate = 9% \[ \text{Unemployed in 1996} = .09 \times 1.2x = .108x \] ### **Step 4: Calculate the Percent Change in the Number of Unemployed Workers** \[ \text{Percent change} = \frac{\text{Final} - \text{Initial}}{\text{Initial}} \times 100\% \] \[ = \frac{.108x - .16x}{.16x} \times 100\% \] \[ = \frac{-.052x}{.16x} \times 100\% \] \[ = \frac{-.052}{.16} \times 100\% \] \[ = -32.5\% \] ### **Step 5: Final Answer** The closest answer is **(B) 30% decrease**. --- ## **Final Answer** ### **(B) 30% decrease**

# Step-by-Step Solution with Explanations Let's break down the problem concerning the unemployment rate among construction workers over the specified time period. ## **Step 1: Assign Variables** Let \( x \) be the total number of construction workers on September 1, 1992. ## **Step 2: Calculate the Number of Workers in 1996** From the problem, we know that the number of construction workers increased by 20% from 1992 to 1996. Therefore, we can express the number of workers in 1996 as: \[ \text{Number of workers in 1996} = x + 0.2x = 1.2x \] ## **Step 3: Calculate the Number of Unemployed Workers in Each Year** ### **Unemployed Workers in 1992** Given that the unemployment rate in 1992 was 16%, the number of unemployed construction workers can be calculated as: \[ \text{Unemployed in 1992} = 0.16x \] ### **Unemployed Workers in 1996** With an unemployment rate of 9% in 1996, we calculate the number of unemployed workers as follows: \[ \text{Unemployed in 1996} = 0.09 \times 1.2x = 0.108x \] ## **Step 4: Calculate the Percent Change in the Number of Unemployed Workers** To find the percentage change in the number of unemployed workers from 1992 to 1996, we use the formula: \[ \text{Percent change} = \frac{\text{Final} - \text{Initial}}{\text{Initial}} \times 100\% \] Substituting the values: \[ \text{Percent change} = \frac{0.108x - 0.16x}{0.16x} \times 100\% \] This simplifies to: \[ = \frac{-0.052x}{0.16x} \times 100\% = \frac{-0.052}{0.16} \times 100\% \] Calculating this gives: \[ = -32.5\% \] ## **Step 5: Interpretation of Results** The negative sign indicates a decrease in the number of unemployed workers. ## **Final Answer** The closest option to the calculated decrease of 32.5% is: ### **(B) 30% decrease**