Small grapefruits	Medium grapefruits	Large grapefruits
$2	$5	$8

Ryan had some grapefruits in 3 sizes. The number of medium grapefruits was thrice the number of large grapefruits. The number of large grapefruits were four times the number of small grapefruits. He sold all the small and medium grapefruits. He received $128 from selling ¹₄ of the large grapefruits.Ryan had some grapefruits in 3 sizes. 
He sold all the small and medium grapefruits. He received $128 from selling ¹₄ 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
	3x4	1x4
1x1		4x1
1 u	12 u	4 u

(a)
The number of large grapefruits is the repeated identity. Make the number of large grapefruits the same.  LCM of 1 and 4 is 4.

	Small grapefruits	Medium grapefruits	Large grapefruits
Before	1 u	12 u	4 u
Change	- 1 u	- 12 u	- 1 u
After	0	0	3 u

Number of large grapefruits that Ryan sold
= ¹₄ x 4 u
= 1 u

	Small grapefruits	Medium grapefruits	Large grapefruits
Number	1 u	12 u	1 u
Value	$2	$5	$8
Total value	2 u	60 u	8 u

Amount that Ryan received from selling of ¹₄ of the large grapefruits = 8 u
8 u = 128

1 u = 128 ÷ 8 = 16

Number of medium grapefruits at first
= 12 u
= 12 x 16
= 192

(b)
Amount that Ryan collected more from selling the medium grapefruits than the small grapefruits
= 60 u - 2 u
= 58 u
= 58 x 16
= $928

Answer(s): (a) 192; (b) $928