Natalie had some fruits at her stall. ³₈ of them were limes, ¹₃ of the remainder were mandarin oranges and the rest were dragon fruits. The amounts earned for each lime, each mandarin orange and each dragon fruit sold are $1.10, $1.60 and $1.80 respectively. The number of limes sold to the number of mandarin oranges sold to the number of dragon fruits sold was 1 : 4 : 3. In total, she sold ¹₁₂ of the fruits and earned $51.60. How many dragon fruits did she have at first?

Limes	Mandarin Oranges	Dragon Fruits	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Limes	Mandarin Oranges	Dragon Fruits
Number	1 u	4 u	3 u
Value	$1.10	$1.60	$1.80
Total value	1.1 u	6.4 u	5.4 u

Total amount that Natalie earned
= 1.1 u + 6.4 u + 5.4 u
= 12.9 u

12.9 u = 51.60
 
1 u = 51.60 ÷ 12.9 = 4

Total number of fruits sold
= 1 u + 4 u + 3 u
= 8 u
= 8 x 4
= 32

Total number of fruits at first
= 32 ÷ ¹₁₂
= 32 x 12
= 384

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

24 p = 384

1 p = 384 ÷ 24 = 16

Number of dragon fruits that Natalie had at first
= 10 p
= 10 x 16
= 160

Answer(s): 160