Janna is creating a multi-tiered cupcake display for a party. She plans on having 16 cupcakes on each tier.
-There is a 1-inch space between all cupcakes.
-The cupcakes have a uniform width [diameter] of 3 inches.
-Each tier will display the cupcakes in either 2 rows of 8, or 4 rows of 4.
-There is a complete 2-inch border, around the cupcakes, on each tier.
Based on this information, which of the following values could be the length and width of each tier?
a.16 inches by 16 inches
b.15 inches by 15 inches
c.19 inches by 19 inches
d.17 inches by 17 inches
To determine the possible length and width of each tier, we need to calculate the total width and length required to accommodate the cupcakes, including the spaces and borders.
First, let's calculate the total width of each tier:
- Each cupcake has a diameter of 3 inches.
- There are 16 cupcakes on each tier.
- There is a 1-inch space between each cupcake.
So, the total width of each tier would be:
Width = (16 cupcakes * 3 inches) + (15 spaces * 1 inch) = 48 inches
Next, let's calculate the total length of each tier:
- Each tier displays cupcakes in either 2 rows of 8 or 4 rows of 4.
- With 2 rows of 8 cupcakes, there are 2 rows, each with 8 cupcakes.
- With 4 rows of 4 cupcakes, there are 4 rows, each with 4 cupcakes.
So, the total length of each tier would be:
Length (2 rows of 8) = (2 rows * (3 inches per cupcake + 1 inch space)) + (2-inch border) = 8 inches + 2 inches = 10 inches
Length (4 rows of 4) = (4 rows * (3 inches per cupcake + 1 inch space)) + (2-inch border) = 16 inches + 2 inches = 18 inches
Based on the information provided, the possible values for the length and width of each tier could be:
- Length: 10 inches, Width: 48 inches (for 2 rows of 8 cupcakes)
- Length: 18 inches, Width: 48 inches (for 4 rows of 4 cupcakes)