Lucy had some fruits at her stall. ³₈ of them were mangosteens, ¹₂ of the remainder were lemons and the rest were pomegranates. The amounts earned for each mangosteen, each lemon and each pomegranate sold are $1.40, $1.50 and $1.70 respectively. The number of mangosteens sold to the number of lemons sold to the number of pomegranates sold was 3 : 3 : 2. In total, she sold ¹₈ of the fruits and earned $169.40. How many pomegranates did she have at first?

Mangosteens	Lemons	Pomegranates	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of lemons and pomegranates is repeated.  Make the total number of lemons and pomegranates the same. LCM of 5 and 2 is 10.

	Mangosteens	Lemons	Pomegranates
Number	3 u	3 u	2 u
Value	$1.40	$1.50	$1.70
Total value	4.2 u	4.5 u	3.4 u

Total amount that Lucy earned
= 4.2 u + 4.5 u + 3.4 u
= 12.1 u

12.1 u = 169.40
 
1 u = 169.40 ÷ 12.1 = 14

Total number of fruits sold
= 3 u + 3 u + 2 u
= 8 u
= 8 x 14
= 112

Total number of fruits at first
= 112 ÷ ¹₈
= 112 x 8
= 896

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 896

1 p = 896 ÷ 16 = 56

Number of pomegranates that Lucy had at first
= 5 p
= 5 x 56
= 280

Answer(s): 280