Cathy had some fruits at her stall. ³₈ of them were mangosteens, ²₃ of the remainder were lemons and the rest were dragon fruits. The amounts earned for each mangosteen, each lemon and each dragon fruit sold are $1.30, $1.40 and $1.60 respectively. The number of mangosteens sold to the number of lemons sold to the number of dragon fruits sold was 5 : 2 : 4. In total, she sold ¹₄ of the fruits and earned $94.20. How many dragon fruits did she have at first?

Mangosteens	Lemons	Dragon Fruits	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

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

	Mangosteens	Lemons	Dragon Fruits
Number	5 u	2 u	4 u
Value	$1.30	$1.40	$1.60
Total value	6.5 u	2.8 u	6.4 u

Total amount that Cathy earned
= 6.5 u + 2.8 u + 6.4 u
= 15.7 u

15.7 u = 94.20
 
1 u = 94.20 ÷ 15.7 = 6

Total number of fruits sold
= 5 u + 2 u + 4 u
= 11 u
= 11 x 6
= 66

Total number of fruits at first
= 66 ÷ ¹₄
= 66 x 4
= 264

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

24 p = 264

1 p = 264 ÷ 24 = 11

Number of dragon fruits that Cathy had at first
= 5 p
= 5 x 11
= 55

Answer(s): 55