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 6.
- Find the total number of soap bars on Day 8.
- Find the total number of soap bars on Day 22.
(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 6
= 4 x 6
2 - 1
= 143
Total number of soap bars on Day 5
= 4 x 5
2 - 1
= 99
Number of 1-cm
3 soap bars added on Day 6
= 143 - 99
= 44
(b)
Number of soap bars on Day 8
= 4 x 8
2 - 1
= 256 - 1
= 255
(c)
Number of soap bars on Day 22
= 4 x 22
2 - 1
= 1936 - 1
= 1935
Answer(s): (a) 44; (b) 255; (c) 1935