Let's tackle each part of the question step-by-step.
### (a) Find the area of the table top in square feet.
First, we need to convert the dimensions of the table from inches to feet. Given that 1 foot is equivalent to 12 inches:
- The length of the table in feet:
[tex]\[
\text{Length in feet} = \frac{84 \text{ inches}}{12 \text{ inches/foot}} = 7 \text{ feet}
\][/tex]
- The width of the table in feet:
[tex]\[
\text{Width in feet} = \frac{36 \text{ inches}}{12 \text{ inches/foot}} = 3 \text{ feet}
\][/tex]
Next, we calculate the area by multiplying the length and width in feet:
[tex]\[
\text{Area} = 7 \text{ feet} \times 3 \text{ feet} = 21 \text{ square feet}
\][/tex]
So, the area of the table top is
[tex]\[
21 \text{ square feet}
\][/tex]
### (b) Determine how many whole bottles of sealant are needed.
Each bottle of sealant covers an area of 13.5 square feet. To find out how many whole bottles are required to cover the table top, we divide the total area by the coverage per bottle and round up to the nearest whole number:
[tex]\[
\text{Number of bottles needed} = \left\lceil \frac{21 \text{ square feet}}{13.5 \text{ square feet/bottle}} \right\rceil
\][/tex]
From the calculation, we find that Heather will need 2 whole bottles of sealant.
So, Heather needs
[tex]\[
2 \text{ bottles}
\][/tex]
### (c) Calculate the total cost of the sealant.
Each bottle of sealant costs [tex]$13.00. If Heather needs 2 bottles, the total cost can be calculated by:
\[
\text{Total cost} = 2 \text{ bottles} \times \$[/tex]13 \text{ per bottle} = \[tex]$26
\]
So, Heather will need to spend:
\[
\$[/tex]26
\]
Summarizing the results:
- The area of the table top is [tex]\(21 \text{ square feet}\)[/tex].
- Heather needs [tex]\(2 \text{ bottles of sealant}\)[/tex].
- The total cost for the sealant is [tex]\(\$26\)[/tex].
