Small grapefruits	Medium grapefruits	Large grapefruits
$4	$5	$7

Justin had some grapefruits in 3 sizes. The number of medium grapefruits was four times the number of large grapefruits. The number of large grapefruits were five times the number of small grapefruits. He sold all the small and medium grapefruits. He received $126 from selling ³₅ of the large grapefruits.

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

Small grapefruits	Medium grapefruits	Large grapefruits
	4x5	1x5
1x1		5x1
1 u	20 u	5 u

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

	Small grapefruits	Medium grapefruits	Large grapefruits
Before	1 u	20 u	5 u
Change	- 1 u	- 20 u	- 3 u
After	0	0	2 u

Number of large grapefruits that Justin sold
= ³₅ x 5 u
= 3 u

	Small grapefruits	Medium grapefruits	Large grapefruits
Number	1 u	20 u	3 u
Value	$4	$5	$7
Total value	4 u	100 u	21 u

Amount that Justin received from selling of ³₅ of the large grapefruits = 21 u
21 u = 126

1 u = 126 ÷ 21 = 6

Number of large grapefruits at first
= 5 u
= 5 x 6
= 30

(b)
Amount that Justin collected less from selling the small grapefruits than the medium grapefruits
= 100 u - 4 u
= 96 u
= 96 x 6
= $576

Answer(s): (a) 30; (b) $576