Question

Kenneth wants to make a quilt out of orange and blue squares of fabric. He plans out the design so that the quilt is 9 pieces long and 12 pieces wide. Here is his sketch.

He sews 2 orange squares followed by 4 blue squares until the quilt is complete. How many blue squares does he need to complete the design?

Answer 1

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.