Small grapefruits	Medium grapefruits	Large grapefruits
$3	$7	$9

Asher had some grapefruits in 3 sizes. The number of medium grapefruits was twice 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 $54 from selling ¹₅ of the large grapefruits.Asher had some grapefruits in 3 sizes. 
He sold all the small and medium grapefruits. He received $54 from selling ¹₅ of the large grapefruits.

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

Small grapefruits	Medium grapefruits	Large grapefruits
	2x5	1x5
1x1		5x1
1 u	10 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	10 u	5 u
Change	- 1 u	- 10 u	- 1 u
After	0	0	4 u

Number of large grapefruits that Asher sold
= ¹₅ x 5 u
= 1 u

	Small grapefruits	Medium grapefruits	Large grapefruits
Number	1 u	10 u	1 u
Value	$3	$7	$9
Total value	3 u	70 u	9 u

Amount that Asher received from selling of ¹₅ of the large grapefruits = 9 u
9 u = 54

1 u = 54 ÷ 9 = 6

Number of medium grapefruits at first
= 10 u
= 10 x 6
= 60

(b)
Amount that Asher collected more from selling the medium grapefruits than the small grapefruits
= 70 u - 3 u
= 67 u
= 67 x 6
= $402

Answer(s): (a) 60; (b) $402