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A rally poster is a rectangle 36 in long and 24 in wide. We want to cover the poster with glitter. The coverage of each tube of glitter is measured in square feet.

(a) Find the area of the poster in square feet.
Use the table of conversion facts, as needed.
[tex]\[ \text{Area} = \square \, \text{ft}^2 \][/tex]

(b) We want to cover the poster with glitter. We don't have any to begin with and we can't buy partial tubes of glitter. Each tube of glitter covers [tex]\[ 0.7 \, \text{ft}^2 \][/tex]. How many whole tubes of glitter will we need to buy in order to completely cover the poster?
[tex]\[ \square \, \text{tubes} \][/tex]

(c) If each tube of glitter costs [tex]\[ \$3 \][/tex], how much will we need to spend on glitter?
[tex]\[ \$ \square \][/tex]

Conversion facts for length:
[tex]\[
\begin{array}{l}
1 \text{ foot } (ft) = 12 \text{ inches } (in) \\
1 \text{ yard } (yd) = 3 \text{ feet } (ft) \\
1 \text{ yard } (yd) = 36 \text{ inches } (in)
\end{array}
\][/tex]



Answer :

GinnyAnswer
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.

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