To determine if Cindy has enough room for all 100 stickers on the poster board, we need to calculate the total area of both the stickers and the poster board.
Step 1: Calculate the area of the stickers
Each sticker is a square with dimensions of 2 inches by 2 inches. The area of one sticker can be calculated as follows:
\[ \text{Area of one sticker} = \text{length} \times \text{width} = 2 , \text{inches} \times 2 , \text{inches} = 4 , \text{square inches} \]
Since Cindy has 100 stickers, the total area for all the stickers is:
\[ \text{Total area of stickers} = 100 \times 4 , \text{square inches} = 400 , \text{square inches} \]
Step 2: Calculate the area of the poster board
The poster board has dimensions of 3 feet by 2 feet. Let's convert these dimensions into inches, because the sticker dimensions are in inches.
1 foot is equal to 12 inches, so:
\[ \text{Length of poster board} = 3 , \text{feet} \times 12 , \text{inches/foot} = 36 , \text{inches} \] \[ \text{Width of poster board} = 2 , \text{feet} \times 12 , \text{inches/foot} = 24 , \text{inches} \]
Next, we calculate the area of the poster board:
\[ \text{Area of poster board} = \text{length} \times \text{width} = 36 , \text{inches} \times 24 , \text{inches} = 864 , \text{square inches} \]
Step 3: Compare the areas
Now we can compare the area of the stickers to the area of the poster board:
- Total area of stickers: \( 400 , \text{square inches} \)
- Total area of poster board: \( 864 , \text{square inches} \)
Conclusion
Since \( 400 , \text{square inches} < 864 , \text{square inches} \), Cindy has enough room for all the stickers on the poster board.