Small peaches	Medium peaches	Large peaches
$4	$6	$8

Vincent had some peaches in 3 sizes. The number of medium peaches was five times the number of large peaches. The number of large peaches were four times the number of small peaches. He sold all the small and medium peaches. He received $112 from selling ¹₄ of the large peaches.Vincent had some peaches in 3 sizes. 
He sold all the small and medium peaches. He received $112 from selling ¹₄ 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
	5x4	1x4
1x1		4x1
1 u	20 u	4 u

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

	Small peaches	Medium peaches	Large peaches
Before	1 u	20 u	4 u
Change	- 1 u	- 20 u	- 1 u
After	0	0	3 u

Number of large peaches that Vincent sold
= ¹₄ x 4 u
= 1 u

	Small peaches	Medium peaches	Large peaches
Number	1 u	20 u	1 u
Value	$4	$6	$8
Total value	4 u	120 u	8 u

Amount that Vincent received from selling of ¹₄ of the large peaches = 8 u
8 u = 112

1 u = 112 ÷ 8 = 14

Number of medium peaches at first
= 20 u
= 20 x 14
= 280

(b)
Amount that Vincent collected more from selling the medium peaches than the small peaches
= 120 u - 4 u
= 116 u
= 116 x 14
= $1624

Answer(s): (a) 280; (b) $1624