Subjects algebra

Apple Trees Ratio E33B3F

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1. **State the problem:** We need to find the relationship between the number of Fuji apple trees (x) and Gala apple trees (y) at Hillsdale Orchard using the given ratio table and plot it on a graph. 2. **Identify the ratio:** From the table, the points are (0,0), (80,30), (160,60), (240,90), (320,120), (400,150), (480,180). We see that for every 80 Fuji trees, there are 30 Gala trees. 3. **Write the ratio as a fraction:** The ratio of Gala to Fuji trees is $$\frac{y}{x} = \frac{30}{80} = \frac{3}{8}$$. 4. **Express y in terms of x:** Using the ratio, the equation relating y and x is $$y = \frac{3}{8}x$$. 5. **Check points:** For example, if $$x=160$$, then $$y = \frac{3}{8} \times 160 = 60$$, which matches the table. 6. **Conclusion:** The graph is a straight line through the origin with slope $$\frac{3}{8}$$ showing the proportional relationship between Fuji and Gala apple trees. **Final equation:** $$y = \frac{3}{8}x$$