Tom placed 22 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 84 cm.
- What was the distance between the first and ninth pin?
- Tom decided to remove 9 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 22 pins
= 22 - 1
= 21
21 intervals = 84 cm
1 interval = 84 ÷ 21 = 4 cm
Number of intervals between the first and the ninth pin = 8
Distance between the first and the ninth pin
= 8 x 4
= 32 cm
(b)
Number of pins left
= 22 - 9
= 13
Number of intervals
= 13 - 1
= 12
New distance of each spacing
= 84 ÷ 12
= 7 cm
Answer(s): (a) 32 cm; (b) 7 cm