Eva had some fruits at her stall. ¹₃ of them were coconuts, ¹₄ of the remainder were plums and the rest were limes. The amounts earned for each coconut, each plum and each lime sold are $1.70, $1.90 and $1.80 respectively. The number of coconuts sold to the number of plums sold to the number of limes sold was 5 : 4 : 4. In total, she sold ¹₂ of the fruits and earned $209.70. How many limes did she have at first?

Coconuts	Plums	Limes	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of plums and limes is repeated.  Make the total number of plums and limes the same. LCM of 2 and 4 is 4.

	Coconuts	Plums	Limes
Number	5 u	4 u	4 u
Value	$1.70	$1.90	$1.80
Total value	8.5 u	7.6 u	7.2 u

Total amount that Eva earned
= 8.5 u + 7.6 u + 7.2 u
= 23.3 u

23.3 u = 209.70
 
1 u = 209.70 ÷ 23.3 = 9

Total number of fruits sold
= 5 u + 4 u + 4 u
= 13 u
= 13 x 9
= 117

Total number of fruits at first
= 117 ÷ ¹₂
= 117 x 2
= 234

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

6 p = 234

1 p = 234 ÷ 6 = 39

Number of limes that Eva had at first
= 3 p
= 3 x 39
= 117

Answer(s): 117