Question

For the home game on Friday, you have to create a banner with a congratulatory message.

The 4-foot tall banner will be 12.5 feet in length. The message will read, "Congratulations!," in all
capital letters.
3 points
Explain how you will create a banner with equally sized letters, leaving no more than 6 inches
of space on either end of the message. In your solution, include the sizes (length and width) of
your letters, and draw a sketch of the finished product, complete with the dimensions (lengths
and widths) labeled.
A three point answer will include how you planned your banner, the explanation for the
dimensions of characters you chose, and a detailed sketch showing labels and dimensions of your
banner.

Answer 1

otal length = 12.5 feet = 12.5 * 12 = 150 inches

Total width = 4 feet = 4 * 12 = 48 inches

We need to leave 6 inches at the ends as border. So the remaining

Length = 150 - (2*6) = 138 inches for 16 characters (CONGRATULATIONS!) which gives 8.625 inches for each character (138 inches divided into 16 parts gives 8.625 inches)

Width = 48 - (2*6) = 36 inches (Height of each Character)

Height of each character = 36 inches

Length of each character = 8.625 inches

With 6 inches border as required.

Explanation:

Answer 2

"Congratulations!" has 16 characters (including the "!")

So you can set up an equation that represents your situation:
c = size of a single character
s = space between characters
r = amount of left over space on a single end

(i changed 12.5 feet to 150 inches)
150 = 16c + 15s + 2r (16 letters + 15 spaces between the letters + 2 * empty space on a single end)

You know you can leave on 6 inches of empty space on either side, so r = 6:

150 = 16c + 15s + 2*6
150 = 16c + 15s + 12
138 = 16 c + 15s

Now you can pick any values for c and s that make the equation true.

For ex: if you pick c = 1 (each letter is 1 inch wide), then
150 = 16 * 1 + 15 s
150 - 16 = 15s
134 = 15s
s = 134/15 ~ 8.93 inches