1. **Stating the problem:** We need to solve questions 3 and 4 using direct and indirect proportion (ratio and proportion). 2. **Understanding direct and indirect proportion:** - Direct proportion means as one quantity increases, the other increases at the same rate. Mathematically, $y \propto x$ or $\frac{y}{x} = k$ where $k$ is a constant. - Indirect (inverse) proportion means as one quantity increases, the other decreases such that their product is constant. Mathematically, $y \propto \frac{1}{x}$ or $xy = k$. 3. **Formulae:** - For direct proportion: $\frac{y_1}{x_1} = \frac{y_2}{x_2}$ - For indirect proportion: $x_1 y_1 = x_2 y_2$ 4. **Applying to question 3:** - Identify if it is direct or indirect proportion. - Use the appropriate formula. - Substitute known values and solve for the unknown. 5. **Applying to question 4:** - Repeat the same steps as question 3. 6. **Example:** - If question 3 states "If 5 pens cost 20 units, how much do 8 pens cost?" this is direct proportion. - Using $\frac{y_1}{x_1} = \frac{y_2}{x_2}$, substitute $\frac{20}{5} = \frac{y_2}{8}$. - Solve for $y_2$: $y_2 = \frac{20}{5} \times 8 = 4 \times 8 = 32$ units. 7. **Example:** - If question 4 states "If 6 workers complete a job in 10 days, how many days will 3 workers take?" this is indirect proportion. - Using $x_1 y_1 = x_2 y_2$, substitute $6 \times 10 = 3 \times y_2$. - Solve for $y_2$: $y_2 = \frac{6 \times 10}{3} = 20$ days. This method can be applied to any direct or indirect proportion problem by identifying the type and using the correct formula.