At Richard's soap factory, a special soap bar - "Johnny's Bricks" is made by adding 1-cm
3 soap bars around the previous day's region of soap bars.
- Find the number of 1-cm3 soap bars added on Day 5.
- Find the total number of soap bars on Day 5.
- Find the total number of soap bars on Day 21.
(a)
Pattern for the number of soap bars
Day 1: 4 x 1
2 - 1 = 3
Day 2: 4 x 2
2 - 1 = 15
Day 3: 4 x 3
2 - 1 = 35
Formula
Number of soap bars = 4 x (Day number)
2 - 1
Total number of soap bars on Day 5
= 4 x 5
2 - 1
= 99
Total number of soap bars on Day 4
= 4 x 4
2 - 1
= 63
Number of 1-cm
3 soap bars added on Day 5
= 99 - 63
= 36
(b)
Number of soap bars on Day 5
= 4 x 5
2 - 1
= 100 - 1
= 99
(c)
Number of soap bars on Day 21
= 4 x 21
2 - 1
= 1764 - 1
= 1763
Answer(s): (a) 36; (b) 99; (c) 1763
