Risa had some fruits at her stall. ³₈ of them were dates, ¹₃ of the remainder were apples and the rest were dragon fruits. The amounts earned for each date, each apple and each dragon fruit sold are $1.30, $1.10 and $1.40 respectively. The number of dates sold to the number of apples sold to the number of dragon fruits sold was 3 : 1 : 2. In total, she sold ¹₁₂ of the fruits and earned $109.20. How many dragon fruits did she have at first?

Dates	Apples	Dragon Fruits	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Dates	Apples	Dragon Fruits
Number	3 u	1 u	2 u
Value	$1.30	$1.10	$1.40
Total value	3.9 u	1.1 u	2.8 u

Total amount that Risa earned
= 3.9 u + 1.1 u + 2.8 u
= 7.8 u

7.8 u = 109.20
 
1 u = 109.20 ÷ 7.8 = 14

Total number of fruits sold
= 3 u + 1 u + 2 u
= 6 u
= 6 x 14
= 84

Total number of fruits at first
= 84 ÷ ¹₁₂
= 84 x 12
= 1008

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

24 p = 1008

1 p = 1008 ÷ 24 = 42

Number of dragon fruits that Risa had at first
= 10 p
= 10 x 42
= 420

Answer(s): 420