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 8.
- Find the total number of soap bars on Day 8.
- Find the total number of soap bars on Day 28.
(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 8
= 4 x 8
2 - 1
= 255
Total number of soap bars on Day 7
= 4 x 7
2 - 1
= 195
Number of 1-cm
3 soap bars added on Day 8
= 255 - 195
= 60
(b)
Number of soap bars on Day 8
= 4 x 8
2 - 1
= 256 - 1
= 255
(c)
Number of soap bars on Day 28
= 4 x 28
2 - 1
= 3136 - 1
= 3135
Answer(s): (a) 60; (b) 255; (c) 3135