To determine how many gray tiles Stacy needs to buy, let's break the problem down step by step.

1. Kitchen Dimensions: The kitchen is 10 feet by 9 feet.
2. Tile Size: Each tile is a 12-inch square, which is equivalent to 1 square foot (since 12 inches = 1 foot).

Step 1: Calculate the Total Area of the Kitchen

The total area of the kitchen is: $\text{Area} = \text{Length} \times \text{Width} = 10 \, \text{ft} \times 9 \, \text{ft} = 90 \, \text{square feet}$ Since each tile covers 1 square foot, we need 90 tiles in total.

Step 2: Analyze the Tile Pattern

From the image, it looks like each pattern block is made up of 6 tiles, with 4 gray tiles and 2 white tiles per pattern block.

Step 3: Determine the Total Number of Pattern Blocks

Since the kitchen has 90 tiles in total, and each pattern block consists of 6 tiles, we can calculate the number of pattern blocks required: $\text{Number of pattern blocks} = \frac{90 \, \text{tiles}}{6 \, \text{tiles per block}} = 15 \, \text{pattern blocks}$

Step 4: Calculate the Number of Gray Tiles

Each pattern block contains 4 gray tiles. So, the total number of gray tiles is: $\text{Total gray tiles} = 15 \, \text{blocks} \times 4 \, \text{gray tiles per block} = 60 \, \text{gray tiles}$

Thus, Stacy needs to buy 60 gray tiles. However, this is not listed among the choices, which suggests that there may be an assumption that tiles must fit exactly without partial blocks or other approximations.

If you'd like further clarification or more details on how this applies to the pattern, feel free to ask!

Related Questions:

1. How would the number of white tiles change if the kitchen size increased?
2. If each tile cost $2, how much would Stacy spend on gray tiles?
3. What is the total cost if Stacy needs to buy both gray and white tiles?
4. How would the pattern adjust if the kitchen size were not a multiple of the pattern block?
5. Can you generalize the method for calculating tiles if the tile size was not 1 square foot?

Tip:

Always check whether pattern blocks fit perfectly into a space when working with repeating designs and tile layouts.