Zeph placed 23 pins in a row from one to the other end of a bulletin board at equal distance apart as shown in the diagram. The distance between the first and last pin was 88 cm.
- What was the distance between the first and eleventh pin?
- Zeph decided to remove 11 pins and rearrange the remaining pins at a new equal spacing. What was the new distance of each spacing?
(a)
Number of intervals is 1 less than the number of pins.
Number of intervals in 23 pins
= 23 - 1
= 22
22 intervals = 88 cm
1 interval = 88 ÷ 22 = 4 cm
Number of intervals between the first and the eleventh pin = 10
Distance between the first and the eleventh pin
= 10 x 4
= 40 cm
(b)
Number of pins left
= 23 - 11
= 12
Number of intervals
= 12 - 1
= 11
New distance of each spacing
= 88 ÷ 11
= 8 cm
Answer(s): (a) 40 cm; (b) 8 cm