Small peaches	Medium peaches	Large peaches
$2	$5	$6

Nick had some peaches in 3 sizes. The number of medium peaches was twice the number of large peaches. The number of large peaches were thrice the number of small peaches. He sold all the small and medium peaches. He received $78 from selling ¹₃ of the large peaches.Nick had some peaches in 3 sizes. 
He sold all the small and medium peaches. He received $78 from selling ¹₃ of the large peaches.

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

Small peaches	Medium peaches	Large peaches
	2x3	1x3
1x1		3x1
1 u	6 u	3 u

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

	Small peaches	Medium peaches	Large peaches
Before	1 u	6 u	3 u
Change	- 1 u	- 6 u	- 1 u
After	0	0	2 u

Number of large peaches that Nick sold
= ¹₃ x 3 u
= 1 u

	Small peaches	Medium peaches	Large peaches
Number	1 u	6 u	1 u
Value	$2	$5	$6
Total value	2 u	30 u	6 u

Amount that Nick received from selling of ¹₃ of the large peaches = 6 u
6 u = 78

1 u = 78 ÷ 6 = 13

Number of medium peaches at first
= 6 u
= 6 x 13
= 78

(b)
Amount that Nick collected more from selling the medium peaches than the small peaches
= 30 u - 2 u
= 28 u
= 28 x 13
= $364

Answer(s): (a) 78; (b) $364