Small durians	Medium durians	Large durians
$2	$8	$9

Ethan had some durians in 3 sizes. The number of medium durians was twice the number of large durians. The number of large durians were thrice the number of small durians. He sold all the small and medium durians. He received $432 from selling ²₃ of the large durians.

1. How many large durians did he have at first?
2. How much less did he collect from selling the small durians than the medium durians?

Small durians	Medium durians	Large durians
	2x3	1x3
1x1		3x1
1 u	6 u	3 u

(a)
The number of large durians is the repeated identity. Make the number of large durians the same.  LCM of 1 and 3 is 3.

	Small durians	Medium durians	Large durians
Before	1 u	6 u	3 u
Change	- 1 u	- 6 u	- 2 u
After	0	0	1 u

Number of large durians that Ethan sold
= ²₃ x 3 u
= 2 u

	Small durians	Medium durians	Large durians
Number	1 u	6 u	2 u
Value	$2	$8	$9
Total value	2 u	48 u	18 u

Amount that Ethan received from selling of ²₃ of the large durians = 18 u
18 u = 432

1 u = 432 ÷ 18 = 24

Number of large durians at first
= 3 u
= 3 x 24
= 72

(b)
Amount that Ethan collected less from selling the small durians than the medium durians
= 48 u - 2 u
= 46 u
= 46 x 24
= $1104

Answer(s): (a) 72; (b) $1104