Shiyun had some fruits at her stall. ¹₃ of them were mangosteens, ¹₃ of the remainder were guavas and the rest were lemons. The amounts earned for each mangosteen, each guava and each lemon sold are $1.90, $1.70 and $1.10 respectively. The number of mangosteens sold to the number of guavas sold to the number of lemons sold was 2 : 1 : 3. In total, she sold ¹₃ of the fruits and earned $123.20. How many lemons did she have at first?

Mangosteens	Guavas	Lemons	Total
1x3	2x3		3x3
	1x2	2x2
3 p	2 p	4 p	9 p

The total number of guavas and lemons is repeated.  Make the total number of guavas and lemons the same. LCM of 2 and 3 is 6.

	Mangosteens	Guavas	Lemons
Number	2 u	1 u	3 u
Value	$1.90	$1.70	$1.10
Total value	3.8 u	1.7 u	3.3 u

Total amount that Shiyun earned
= 3.8 u + 1.7 u + 3.3 u
= 8.8 u

8.8 u = 123.20
 
1 u = 123.20 ÷ 8.8 = 14

Total number of fruits sold
= 2 u + 1 u + 3 u
= 6 u
= 6 x 14
= 84

Total number of fruits at first
= 84 ÷ ¹₃
= 84 x 3
= 252

Total number of fruits at first
= 3 p + 2 p + 4 p
= 9 p

9 p = 252

1 p = 252 ÷ 9 = 28

Number of lemons that Shiyun had at first
= 4 p
= 4 x 28
= 112

Answer(s): 112