Answer :
To determine how many square feet Shelly can cover with her paint, we will break down the problem into a series of steps:
1. Convert the mixed number of paint cans to a decimal:
Shelly has [tex]\(2 \frac{3}{4}\)[/tex] cans of paint. To convert this mixed number to a decimal:
[tex]\[
2 \frac{3}{4} = 2 + \frac{3}{4}
\][/tex]
The fraction [tex]\(\frac{3}{4}\)[/tex] as a decimal is [tex]\(0.75\)[/tex], therefore:
[tex]\[
2 \frac{3}{4} = 2 + 0.75 = 2.75
\][/tex]
So, Shelly has 2.75 cans of paint.
2. Determine the coverage of each can of paint:
Each can of paint covers 35.5 square feet.
3. Calculate the total area that can be painted with 2.75 cans:
To find the total coverage, multiply the number of cans by the coverage per can:
[tex]\[
\text{Total coverage} = 2.75 \text{ cans} \times 35.5 \text{ square feet per can}
\][/tex]
When multiplying these together, we get:
[tex]\[
\text{Total coverage} = 97.625 \text{ square feet}
\][/tex]
4. Convert the total coverage to a mixed number:
To express 97.625 as a mixed number:
[tex]\[
97.625 = 97 + 0.625
\][/tex]
The decimal [tex]\(0.625\)[/tex] can be converted to a fraction. Since [tex]\(0.625\)[/tex] is equivalent to [tex]\(\frac{625}{1000}\)[/tex], which simplifies to [tex]\(\frac{5}{8}\)[/tex]:
[tex]\[
97.625 = 97 \frac{5}{8}
\][/tex]
5. Compare this with the provided choices:
- A: [tex]\(71 \frac{3}{4}\)[/tex]
- B: [tex]\(97 \frac{5}{8}\)[/tex]
- C: [tex]\(70 \frac{1}{4}\)[/tex]
- D: [tex]\(88 \frac{3}{4}\)[/tex]
The total coverage exactly matches option [tex]\(B: 97 \frac{5}{8}\)[/tex].
Therefore, Shelly can cover [tex]\(97 \frac{5}{8}\)[/tex] square feet with the paint she has. Option B is the correct answer.
1. Convert the mixed number of paint cans to a decimal:
Shelly has [tex]\(2 \frac{3}{4}\)[/tex] cans of paint. To convert this mixed number to a decimal:
[tex]\[
2 \frac{3}{4} = 2 + \frac{3}{4}
\][/tex]
The fraction [tex]\(\frac{3}{4}\)[/tex] as a decimal is [tex]\(0.75\)[/tex], therefore:
[tex]\[
2 \frac{3}{4} = 2 + 0.75 = 2.75
\][/tex]
So, Shelly has 2.75 cans of paint.
2. Determine the coverage of each can of paint:
Each can of paint covers 35.5 square feet.
3. Calculate the total area that can be painted with 2.75 cans:
To find the total coverage, multiply the number of cans by the coverage per can:
[tex]\[
\text{Total coverage} = 2.75 \text{ cans} \times 35.5 \text{ square feet per can}
\][/tex]
When multiplying these together, we get:
[tex]\[
\text{Total coverage} = 97.625 \text{ square feet}
\][/tex]
4. Convert the total coverage to a mixed number:
To express 97.625 as a mixed number:
[tex]\[
97.625 = 97 + 0.625
\][/tex]
The decimal [tex]\(0.625\)[/tex] can be converted to a fraction. Since [tex]\(0.625\)[/tex] is equivalent to [tex]\(\frac{625}{1000}\)[/tex], which simplifies to [tex]\(\frac{5}{8}\)[/tex]:
[tex]\[
97.625 = 97 \frac{5}{8}
\][/tex]
5. Compare this with the provided choices:
- A: [tex]\(71 \frac{3}{4}\)[/tex]
- B: [tex]\(97 \frac{5}{8}\)[/tex]
- C: [tex]\(70 \frac{1}{4}\)[/tex]
- D: [tex]\(88 \frac{3}{4}\)[/tex]
The total coverage exactly matches option [tex]\(B: 97 \frac{5}{8}\)[/tex].
Therefore, Shelly can cover [tex]\(97 \frac{5}{8}\)[/tex] square feet with the paint she has. Option B is the correct answer.
