Small grapefruits	Medium grapefruits	Large grapefruits
$3	$5	$7

Elijah had some grapefruits in 3 sizes. The number of medium grapefruits was five times the number of large grapefruits. The number of large grapefruits were thrice the number of small grapefruits. He sold all the small and medium grapefruits. He received $210 from selling ²₃ 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
	5x3	1x3
1x1		3x1
1 u	15 u	3 u

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

	Small grapefruits	Medium grapefruits	Large grapefruits
Before	1 u	15 u	3 u
Change	- 1 u	- 15 u	- 2 u
After	0	0	1 u

Number of large grapefruits that Elijah sold
= ²₃ x 3 u
= 2 u

	Small grapefruits	Medium grapefruits	Large grapefruits
Number	1 u	15 u	2 u
Value	$3	$5	$7
Total value	3 u	75 u	14 u

Amount that Elijah received from selling of ²₃ of the large grapefruits = 14 u
14 u = 210

1 u = 210 ÷ 14 = 15

Number of large grapefruits at first
= 3 u
= 3 x 15
= 45

(b)
Amount that Elijah collected less from selling the small grapefruits than the medium grapefruits
= 75 u - 3 u
= 72 u
= 72 x 15
= $1080

Answer(s): (a) 45; (b) $1080