Small mangoes	Medium mangoes	Large mangoes
$2	$6	$9

Neave had some mangoes in 3 sizes. The number of medium mangoes was twice the number of large mangoes. The number of large mangoes were thrice the number of small mangoes. He sold all the small and medium mangoes. He received $234 from selling ²₃ of the large mangoes.Neave had some mangoes in 3 sizes. 
He sold all the small and medium mangoes. He received $234 from selling ²₃ of the large mangoes.

1. How many medium mangoes did he have at first?
2. How much more did he collect from selling the medium mangoes than the small mangoes?

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

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

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

Number of large mangoes that Neave sold
= ²₃ x 3 u
= 2 u

	Small mangoes	Medium mangoes	Large mangoes
Number	1 u	6 u	2 u
Value	$2	$6	$9
Total value	2 u	36 u	18 u

Amount that Neave received from selling of ²₃ of the large mangoes = 18 u
18 u = 234

1 u = 234 ÷ 18 = 13

Number of medium mangoes at first
= 6 u
= 6 x 13
= 78

(b)
Amount that Neave collected more from selling the medium mangoes than the small mangoes
= 36 u - 2 u
= 34 u
= 34 x 13
= $442

Answer(s): (a) 78; (b) $442