Question

A high school principal wants to hang four league championship banners on an 84 foot long cafeteria wall. The banners are each
12
1
2
feet wide and must be placed either
4
1
2
feet or
6
1
2
feet from the left and right edges of the wall.

What could the space between the banners be if the spacing is equal between each banner? Select all that apply.


5
1
4
feet


6
1
4
feet


7
feet


8
1
3
feet


11
1
3
feet

Answer 1

Let s be the equal spacing between banners. The four banners use 4 × 12 1/2 = 50 ft, so

left + right + 3s + 50 = 84 ⇒ 3s = 34 − (left + right) ⇒ s = (34 − (left + right)) / 3.

left and right can each be 4 1/2 (=9/2) or 6 1/2 (=13/2), so left+right can be 9, 11, or 13:

- If left+right = 9: s = (34 − 9)/3 = 25/3 = 8 1/3 ft.
- If left+right = 11: s = (34 − 11)/3 = 23/3 = 7 2/3 ft (not listed).
- If left+right = 13: s = (34 − 13)/3 = 21/3 = 7 ft.

Thus the possible spacings from the choices are 8 1/3 ft and 7 ft.