Subjects algebra

Proportion Questions 7Ab5F5

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1. Problem Q11: If 5 workers can complete a task in 4 days, how many days will it take 10 workers, assuming the same efficiency? 2. Formula: The work done is constant, so $\text{Workers} \times \text{Days} = \text{Constant}$. 3. Calculation for Q11: $$5 \times 4 = 10 \times d$$ where $d$ is the number of days for 10 workers. 4. Solve for $d$: $$d = \frac{5 \times 4}{10}$$ 5. Simplify: $$d = \frac{\cancel{5} \times 4}{\cancel{10}} = \frac{4}{2} = 2$$ 6. Answer for Q11: It will take 10 workers 2 days to complete the task. 7. Problem Q12: If 6 machines produce 300 units, how many units will 12 machines produce under the same conditions? 8. Formula: Production is proportional to the number of machines, so $\frac{\text{Units}_1}{\text{Machines}_1} = \frac{\text{Units}_2}{\text{Machines}_2}$. 9. Calculation for Q12: $$\frac{300}{6} = \frac{x}{12}$$ where $x$ is the units produced by 12 machines. 10. Solve for $x$: $$x = \frac{300 \times 12}{6}$$ 11. Simplify: $$x = 300 \times \frac{\cancel{12}}{\cancel{6}} = 300 \times 2 = 600$$ 12. Answer for Q12: 12 machines will produce 600 units.