Fiona had some fruits at her stall. ¹₃ of them were plums, ¹₃ of the remainder were lemons and the rest were pomegranates. The amounts earned for each plum, each lemon and each pomegranate sold are $1.20, $1.90 and $1.10 respectively. The number of plums sold to the number of lemons sold to the number of pomegranates sold was 4 : 3 : 3. In total, she sold ¹₃ of the fruits and earned $165.60. How many pomegranates did she have at first?

Plums	Lemons	Pomegranates	Total
1x3	2x3		3x3
	1x2	2x2
3 p	2 p	4 p	9 p

The total number of lemons and pomegranates is repeated.  Make the total number of lemons and pomegranates the same. LCM of 2 and 3 is 6.

	Plums	Lemons	Pomegranates
Number	4 u	3 u	3 u
Value	$1.20	$1.90	$1.10
Total value	4.8 u	5.7 u	3.3 u

Total amount that Fiona earned
= 4.8 u + 5.7 u + 3.3 u
= 13.8 u

13.8 u = 165.60
 
1 u = 165.60 ÷ 13.8 = 12

Total number of fruits sold
= 4 u + 3 u + 3 u
= 10 u
= 10 x 12
= 120

Total number of fruits at first
= 120 ÷ ¹₃
= 120 x 3
= 360

Total number of fruits at first
= 3 p + 2 p + 4 p
= 9 p

9 p = 360

1 p = 360 ÷ 9 = 40

Number of pomegranates that Fiona had at first
= 4 p
= 4 x 40
= 160

Answer(s): 160