Erika had some fruits at her stall. ¹₃ of them were kiwis, ¹₄ of the remainder were pomegranates and the rest were dragon fruits. The amounts earned for each kiwi, each pomegranate and each dragon fruit sold are $1.70, $1.10 and $1.80 respectively. The number of kiwis sold to the number of pomegranates sold to the number of dragon fruits sold was 2 : 1 : 1. In total, she sold ¹₃ of the fruits and earned $37.80. How many dragon fruits did she have at first?

Kiwis	Pomegranates	Dragon Fruits	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of pomegranates and dragon fruits is repeated.  Make the total number of pomegranates and dragon fruits the same. LCM of 2 and 4 is 4.

	Kiwis	Pomegranates	Dragon Fruits
Number	2 u	1 u	1 u
Value	$1.70	$1.10	$1.80
Total value	3.4 u	1.1 u	1.8 u

Total amount that Erika earned
= 3.4 u + 1.1 u + 1.8 u
= 6.3 u

6.3 u = 37.80
 
1 u = 37.80 ÷ 6.3 = 6

Total number of fruits sold
= 2 u + 1 u + 1 u
= 4 u
= 4 x 6
= 24

Total number of fruits at first
= 24 ÷ ¹₃
= 24 x 3
= 72

Total number of fruits at first
= 2 p + 1 p + 3 p
= 6 p

6 p = 72

1 p = 72 ÷ 6 = 12

Number of dragon fruits that Erika had at first
= 3 p
= 3 x 12
= 36

Answer(s): 36