Hilda had some fruits at her stall. ³₈ of them were apricots, ¹₄ of the remainder were grapefruits and the rest were dragon fruits. The amounts earned for each apricot, each grapefruit and each dragon fruit sold are $1.50, $1.60 and $1.30 respectively. The number of apricots sold to the number of grapefruits sold to the number of dragon fruits sold was 1 : 1 : 4. In total, she sold ¹₁₆ of the fruits and earned $149.40. How many dragon fruits did she have at first?

Apricots	Grapefruits	Dragon Fruits	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of grapefruits and dragon fruits is repeated.  Make the total number of grapefruits and dragon fruits the same. LCM of 5 and 4 is 20.

	Apricots	Grapefruits	Dragon Fruits
Number	1 u	1 u	4 u
Value	$1.50	$1.60	$1.30
Total value	1.5 u	1.6 u	5.2 u

Total amount that Hilda earned
= 1.5 u + 1.6 u + 5.2 u
= 8.3 u

8.3 u = 149.40
 
1 u = 149.40 ÷ 8.3 = 18

Total number of fruits sold
= 1 u + 1 u + 4 u
= 6 u
= 6 x 18
= 108

Total number of fruits at first
= 108 ÷ ¹₁₆
= 108 x 16
= 1728

Total number of fruits at first
= 12 p + 5 p + 15 p
= 32 p

32 p = 1728

1 p = 1728 ÷ 32 = 54

Number of dragon fruits that Hilda had at first
= 15 p
= 15 x 54
= 810

Answer(s): 810