1. **State the problem:** We need to determine who has the better deal for printing photographs between Hana and Freya. 2. **Understand the concept:** The cost is directly proportional to the number of photographs. This means cost per photograph is constant. 3. **Formula:** Cost per photograph = \frac{Total cost}{Number of photographs} 4. **Calculate Hana's cost per photograph:** $$\text{Hana's cost per photo} = \frac{16.50}{150} = 0.11$$ 5. **Calculate Freya's cost per photograph:** $$\text{Freya's cost per photo} = \frac{9.60}{80} = 0.12$$ 6. **Compare the costs:** Hana pays 0.11 per photo, Freya pays 0.12 per photo. 7. **Conclusion:** Hana has the better deal because her cost per photograph is lower. --- 1. **State the problem:** Given readings of variables $x$ and $y$, determine if $y$ is directly proportional to $x$. 2. **Data:** \begin{align*} x &: 1.3, 2.4, 2.6 \\ y &: 10.4, 19.2, 20.8 \end{align*} 3. **Check direct proportionality:** If $y = kx$, then $\frac{y}{x} = k$ should be constant. 4. **Calculate ratios:** $$\frac{10.4}{1.3} = 8$$ $$\frac{19.2}{2.4} = 8$$ $$\frac{20.8}{2.6} = 8$$ 5. **Interpretation:** Since all ratios are equal to 8, $y$ is directly proportional to $x$ with constant $k=8$. 6. **Formula:** $$y = 8x$$ 7. **Conclusion:** The data confirms a direct proportionality between $y$ and $x$ with proportionality constant 8.