Dana had some fruits at her stall. ¹₃ of them were coconuts, ¹₄ of the remainder were peaches and the rest were apples. The amounts earned for each coconut, each peach and each apple sold are $1.60, $1.90 and $1.80 respectively. The number of coconuts sold to the number of peaches sold to the number of apples sold was 1 : 2 : 3. In total, she sold ¹₂ of the fruits and earned $97.20. How many apples did she have at first?

Coconuts	Peaches	Apples	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of peaches and apples is repeated.  Make the total number of peaches and apples the same. LCM of 2 and 4 is 4.

	Coconuts	Peaches	Apples
Number	1 u	2 u	3 u
Value	$1.60	$1.90	$1.80
Total value	1.6 u	3.8 u	5.4 u

Total amount that Dana earned
= 1.6 u + 3.8 u + 5.4 u
= 10.8 u

10.8 u = 97.20
 
1 u = 97.20 ÷ 10.8 = 9

Total number of fruits sold
= 1 u + 2 u + 3 u
= 6 u
= 6 x 9
= 54

Total number of fruits at first
= 54 ÷ ¹₂
= 54 x 2
= 108

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

6 p = 108

1 p = 108 ÷ 6 = 18

Number of apples that Dana had at first
= 3 p
= 3 x 18
= 54

Answer(s): 54