Let's solve each part of the question step-by-step:
### Part (a) - Find the area of the poster in square feet.
1. Convert the dimensions of the poster to feet:
- The poster is 36 inches long and 24 inches wide.
- There are 12 inches in 1 foot.
- To convert inches to feet:
[tex]\[
\text{Length in feet} = \frac{36 \text{ in}}{12 \text{ in/ft}} = 3 \text{ ft}
\][/tex]
[tex]\[
\text{Width in feet} = \frac{24 \text{ in}}{12 \text{ in/ft}} = 2 \text{ ft}
\][/tex]
2. Calculate the area of the poster in square feet:
- Area is calculated by multiplying the length and the width.
[tex]\[
\text{Area} = \text{Length} \times \text{Width} = 3 \text{ ft} \times 2 \text{ ft} = 6 \text{ ft}^2
\][/tex]
So, the area of the poster is [tex]\( 6 \text{ ft}^2 \)[/tex].
### Part (b) - Number of whole tubes of glitter needed.
1. Determine how many tubes of glitter are needed:
- Each tube of glitter covers [tex]\( 0.7 \text{ ft}^2 \)[/tex].
- Total area to cover is [tex]\( 6 \text{ ft}^2 \)[/tex].
- Number of tubes needed:
[tex]\[
\text{Number of tubes} = \frac{\text{Total area}}{\text{Coverage per tube}} = \frac{6 \text{ ft}^2}{0.7 \text{ ft}^2/\text{tube}} \approx 8.571
\][/tex]
2. Since we can't buy partial tubes, we round up to the nearest whole number:
- Therefore, we need [tex]\( 9 \)[/tex] tubes of glitter.
So, we need to buy [tex]\( 9 \)[/tex] tubes of glitter to cover the poster.
### Part (c) - Total cost of the glitter.
1. Calculate the total cost:
- Each tube of glitter costs [tex]$3.
- Number of tubes needed is \( 9 \).
- Total cost:
\[
\text{Total cost} = \text{Number of tubes} \times \text{Cost per tube} = 9 \times 3 = 27
\]
So, the total cost will be $[/tex]27.
### Summary:
(a) The area of the poster is [tex]\( 6 \text{ ft}^2 \)[/tex].
(b) We need to buy [tex]\( 9 \)[/tex] tubes of glitter.
(c) The total cost of the glitter is $27.
