Cindy had some fruits at her stall. ³₈ of them were plums, ¹₃ of the remainder were dragon fruits and the rest were pomegranates. The amounts earned for each plum, each dragon fruit and each pomegranate sold are $1.40, $1.80 and $1.20 respectively. The number of plums sold to the number of dragon fruits sold to the number of pomegranates sold was 4 : 3 : 2. In total, she sold ¹₄ of the fruits and earned $214.40. How many plums did she have at first?

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

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

	Plums	Dragon Fruits	Pomegranates
Number	4 u	3 u	2 u
Value	$1.40	$1.80	$1.20
Total value	5.6 u	5.4 u	2.4 u

Total amount that Cindy earned
= 5.6 u + 5.4 u + 2.4 u
= 13.4 u

13.4 u = 214.40
 
1 u = 214.40 ÷ 13.4 = 16

Total number of fruits sold
= 4 u + 3 u + 2 u
= 9 u
= 9 x 16
= 144

Total number of fruits at first
= 144 ÷ ¹₄
= 144 x 4
= 576

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

24 p = 576

1 p = 576 ÷ 24 = 24

Number of plums that Cindy had at first
= 9 p
= 9 x 24
= 216

Answer(s): 216