Jane had some fruits at her stall. ¹₃ of them were limes, ³₄ of the remainder were mangosteens and the rest were guavas. The amounts earned for each lime, each mangosteen and each guava sold are $1.90, $1.80 and $1.20 respectively. The number of limes sold to the number of mangosteens sold to the number of guavas sold was 4 : 1 : 1. In total, she sold ¹₃ of the fruits and earned $95.40. How many limes did she have at first?

Limes	Mangosteens	Guavas	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of mangosteens and guavas is repeated.  Make the total number of mangosteens and guavas the same. LCM of 2 and 4 is 4.

	Limes	Mangosteens	Guavas
Number	4 u	1 u	1 u
Value	$1.90	$1.80	$1.20
Total value	7.6 u	1.8 u	1.2 u

Total amount that Jane earned
= 7.6 u + 1.8 u + 1.2 u
= 10.6 u

10.6 u = 95.40
 
1 u = 95.40 ÷ 10.6 = 9

Total number of fruits sold
= 4 u + 1 u + 1 u
= 6 u
= 6 x 9
= 54

Total number of fruits at first
= 54 ÷ ¹₃
= 54 x 3
= 162

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

6 p = 162

1 p = 162 ÷ 6 = 27

Number of limes that Jane had at first
= 2 p
= 2 x 27
= 54

Answer(s): 54