Cindy is making a display for a project. She plans on placing 100 stickers that are 2 in by 2-inch squares on a poster board. The poster board she is using has a length of 3 feet and a width of 2 feet. Does she have enough room for all the stickers?

SHOW WORK

1 answer

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.