Lucy had some fruits at her stall. ³₈ of them were plums, ¹₃ of the remainder were dragon fruits and the rest were apricots. The amounts earned for each plum, each dragon fruit and each apricot sold are $1.30, $1.20 and $1.60 respectively. The number of plums sold to the number of dragon fruits sold to the number of apricots sold was 1 : 2 : 1. In total, she sold ¹₆ of the fruits and earned $21.20. How many plums did she have at first?

Plums	Dragon Fruits	Apricots	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of dragon fruits and apricots is repeated.  Make the total number of dragon fruits and apricots the same. LCM of 5 and 3 is 15.

	Plums	Dragon Fruits	Apricots
Number	1 u	2 u	1 u
Value	$1.30	$1.20	$1.60
Total value	1.3 u	2.4 u	1.6 u

Total amount that Lucy earned
= 1.3 u + 2.4 u + 1.6 u
= 5.3 u

5.3 u = 21.20
 
1 u = 21.20 ÷ 5.3 = 4

Total number of fruits sold
= 1 u + 2 u + 1 u
= 4 u
= 4 x 4
= 16

Total number of fruits at first
= 16 ÷ ¹₆
= 16 x 6
= 96

Total number of fruits at first
= 9 p + 5 p + 10 p
= 24 p

24 p = 96

1 p = 96 ÷ 24 = 4

Number of plums that Lucy had at first
= 9 p
= 9 x 4
= 36

Answer(s): 36