1. **Problem statement:** Jon is tiling a 2-foot wide border around a bathtub that measures 5 feet by 3 feet. Each tile measures 4 inches by 4 inches. We need to find the minimum number of tiles Jon needs. 2. **Step 1: Calculate the outer dimensions of the tiled area.** The border is 2 feet wide around the tub, so add 2 feet on each side: $$\text{Outer length} = 5 + 2 \times 2 = 9 \text{ feet}$$ $$\text{Outer width} = 3 + 2 \times 2 = 7 \text{ feet}$$ 3. **Step 2: Calculate the area of the outer rectangle (bathtub + border).** $$\text{Outer area} = 9 \times 7 = 63 \text{ square feet}$$ 4. **Step 3: Calculate the area of the bathtub (inner rectangle).** $$\text{Inner area} = 5 \times 3 = 15 \text{ square feet}$$ 5. **Step 4: Calculate the area of the border (area to be tiled).** $$\text{Border area} = \text{Outer area} - \text{Inner area} = 63 - 15 = 48 \text{ square feet}$$ 6. **Step 5: Convert tile dimensions to feet.** Since 1 foot = 12 inches, $$4 \text{ inches} = \frac{4}{12} = \frac{1}{3} \text{ feet}$$ 7. **Step 6: Calculate the area of one tile.** $$\text{Tile area} = \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) = \frac{1}{9} \text{ square feet}$$ 8. **Step 7: Calculate the number of tiles needed.** $$\text{Number of tiles} = \frac{\text{Border area}}{\text{Tile area}} = \frac{48}{\frac{1}{9}} = 48 \times 9 = 432$$ 9. **Step 8: Conclusion** Jon needs a minimum of **432 tiles** to cover the 2-foot border around the bathtub.