Small mangoes	Medium mangoes	Large mangoes
$2	$5	$9

Ethan had some mangoes in 3 sizes. The number of medium mangoes was twice the number of large mangoes. The number of large mangoes were five times the number of small mangoes. He sold all the small and medium mangoes. He received $432 from selling ³₅ of the large mangoes.

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

Small mangoes	Medium mangoes	Large mangoes
	2x5	1x5
1x1		5x1
1 u	10 u	5 u

(a)
The number of large mangoes is the repeated identity. Make the number of large mangoes the same.  LCM of 1 and 5 is 5.

	Small mangoes	Medium mangoes	Large mangoes
Before	1 u	10 u	5 u
Change	- 1 u	- 10 u	- 3 u
After	0	0	2 u

Number of large mangoes that Ethan sold
= ³₅ x 5 u
= 3 u

	Small mangoes	Medium mangoes	Large mangoes
Number	1 u	10 u	3 u
Value	$2	$5	$9
Total value	2 u	50 u	27 u

Amount that Ethan received from selling of ³₅ of the large mangoes = 27 u
27 u = 432

1 u = 432 ÷ 27 = 16

Number of large mangoes at first
= 5 u
= 5 x 16
= 80

(b)
Amount that Ethan collected less from selling the small mangoes than the medium mangoes
= 50 u - 2 u
= 48 u
= 48 x 16
= $768

Answer(s): (a) 80; (b) $768