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.
