To determine how many blue squares Kenneth needs for his quilt, we first need to calculate the total number of squares in the quilt.
The dimensions of the quilt are:
- Length: 9 pieces
- Width: 12 pieces
The total number of squares in the quilt can be calculated as follows:
\[ \text{Total squares} = \text{Length} \times \text{Width} = 9 \times 12 = 108 \text{ squares} \]
Next, we analyze the pattern in which Kenneth sews his squares:
- He uses 2 orange squares followed by 4 blue squares in a repeating pattern.
This pattern contains a total of:
\[ \text{Total squares in one pattern} = 2 \text{ (orange)} + 4 \text{ (blue)} = 6 \text{ squares} \]
Now, we need to find out how many complete patterns fit within the total of 108 squares:
\[ \text{Number of complete patterns} = \frac{\text{Total squares}}{\text{Squares per pattern}} = \frac{108}{6} = 18 \]
Now we can calculate the total number of blue squares. In each complete pattern, there are 4 blue squares. Thus, the total number of blue squares needed for the entire quilt is:
\[ \text{Total blue squares} = \text{Number of complete patterns} \times \text{Blue squares per pattern} = 18 \times 4 = 72 \]
Therefore, Kenneth needs 72 blue squares to complete the quilt design.
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