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 9.
- Find the total number of soap bars on Day 11.
- Find the total number of soap bars on Day 27.
(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 9
= 4 x 9
2 - 1
= 323
Total number of soap bars on Day 8
= 4 x 8
2 - 1
= 255
Number of 1-cm
3 soap bars added on Day 9
= 323 - 255
= 68
(b)
Number of soap bars on Day 11
= 4 x 11
2 - 1
= 484 - 1
= 483
(c)
Number of soap bars on Day 27
= 4 x 27
2 - 1
= 2916 - 1
= 2915
Answer(s): (a) 68; (b) 483; (c) 2915