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3. Phyllis and Audra are making a quilt for their grandmother with squares of colored fabric. So far, they have made 118 squares, each with a 4-inch-long side. Their grandmother's bed measures 5 ft by [tex]\(6 \frac{1}{2}\)[/tex] ft.

Part A: What are the dimensions of their grandmother's bed in inches?
[tex]\[
\begin{array}{l}
5 \times 12 = 60 \\
6.5 \times 12 = 78 \\
\text{The dimensions of the bed are 60 inches by 78 inches.}
\end{array}
\][/tex]

Part C: What is the total area of the quilt squares created so far? (in square inches)

The area of the quilt so far is [tex]\(\quad\)[/tex] square inches.

Part D: How many more squares will Phyllis and Audra have to make to completely cover the top of their grandmother's bed?

Phyllis and Audra will need [tex]\(\quad\)[/tex] more squares.



Answer :

GinnyAnswer
Let's go through each part step-by-step:

Part A: Converting the dimensions of their grandmother's bed to inches

First, we need to convert the dimensions from feet to inches. We know that:

- One foot is equal to 12 inches.

The given dimensions of the bed are:
- 5 feet in length
- [tex]\(6 \frac{1}{2}\)[/tex] feet in width (which is equal to 6.5 feet)

To convert these to inches:

1. The length:
[tex]\[ 5 \text{ feet} \times 12 \text{ inches/foot} = 60 \text{ inches} \][/tex]

2. The width:
[tex]\[ 6.5 \text{ feet} \times 12 \text{ inches/foot} = 78 \text{ inches} \][/tex]

Thus, the dimensions of their grandmother's bed are 60 inches by 78 inches.

Part C: Calculating the total area of the quilt squares created so far

Each square has a side length of 4 inches. The area of one square can be found by squaring the side length:

[tex]\[ \text{Area of one square} = \text{side}^2 = 4 \text{ inches} \times 4 \text{ inches} = 16 \text{ square inches} \][/tex]

Phyllis and Audra have made 118 squares so far. The total area of all the quilt squares is:

[tex]\[ \text{Total area} = \text{number of squares} \times \text{area of one square} = 118 \times 16 = 1888 \text{ square inches} \][/tex]

The area of the quilt so far is 1888 square inches.

Part D: Determining how many more squares are needed to cover the bed

The next step is to determine the total area of the bed in square inches:

[tex]\[ \text{Total area of the bed} = \text{length} \times \text{width} = 60 \text{ inches} \times 78 \text{ inches} = 4680 \text{ square inches} \][/tex]

To find out how many quilt squares are needed to cover the bed, we divide the total area of the bed by the area of one quilt square:

[tex]\[ \text{Number of squares needed} = \frac{\text{Total area of the bed}}{\text{Area of one square}} = \frac{4680}{16} = 292.5 \][/tex]

Since we cannot have a fraction of a square, we will need 293 squares to fully cover the bed.

Finally, we need to determine how many more squares Phyllis and Audra need to make. They have already made 118 squares:

[tex]\[ \text{More squares needed} = \text{Number of squares needed} - \text{Number of squares made} = 293 - 118 = 175 \][/tex]

Therefore, Phyllis and Audra will need 175 more squares to completely cover the top of their grandmother's bed.

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