Subjects algebra

Employees Stamping 1C0611

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1. **State the problem:** We know that in 2005, the Product Development department had 150 employees, which is 25% less than in 2000. We need to find how many employees worked in the Stamping department in 2000. 2. **Understand the relationship:** If the number of employees in Product Development in 2005 is 25% less than in 2000, then: $$\text{Employees in 2005} = \text{Employees in 2000} - 0.25 \times \text{Employees in 2000} = 0.75 \times \text{Employees in 2000}$$ 3. **Calculate employees in Product Development in 2000:** Let $x$ be the number of employees in Product Development in 2000. $$150 = 0.75x$$ Divide both sides by 0.75: $$150 = \cancel{0.75}x \div \cancel{0.75} \Rightarrow x = \frac{150}{0.75}$$ $$x = 200$$ So, there were 200 employees in Product Development in 2000. 4. **Use the total percentage to find Stamping employees in 2000:** From the problem context (implied from the original data), the Stamping department constituted 20% of employees in 2000. 5. **Calculate total employees in 2000:** Since Product Development was 29% in 2000 and had 200 employees, total employees in 2000 can be found by: $$\text{Total employees} = \frac{200}{0.29} \approx 689.66$$ 6. **Calculate employees in Stamping in 2000:** Stamping was 20% of total employees in 2000: $$\text{Stamping employees} = 0.20 \times 689.66 \approx 137.93$$ 7. **Check options:** None of the options match 138 approximately, so the answer is E. None of these. **Final answer:** E. None of these