Answered

IDNLearn.com provides a user-friendly platform for finding and sharing knowledge. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

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.

Sagot :

GinnyAnsweridn
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.