Yen had some fruits at her stall. ¹₃ of them were lemons, ²₃ of the remainder were kiwis and the rest were tomatoes. The amounts earned for each lemon, each kiwi and each tomato sold are $1.10, $1.40 and $1.90 respectively. The number of lemons sold to the number of kiwis sold to the number of tomatoes sold was 5 : 2 : 5. In total, she sold ¹₃ of the fruits and earned $53.40. How many lemons did she have at first?

Lemons	Kiwis	Tomatoes	Total
1x3	2x3		3x3
	2x2	1x2
3 p	4 p	2 p	9 p

The total number of kiwis and tomatoes is repeated.  Make the total number of kiwis and tomatoes the same. LCM of 2 and 3 is 6.

	Lemons	Kiwis	Tomatoes
Number	5 u	2 u	5 u
Value	$1.10	$1.40	$1.90
Total value	5.5 u	2.8 u	9.5 u

Total amount that Yen earned
= 5.5 u + 2.8 u + 9.5 u
= 17.8 u

17.8 u = 53.40
 
1 u = 53.40 ÷ 17.8 = 3

Total number of fruits sold
= 5 u + 2 u + 5 u
= 12 u
= 12 x 3
= 36

Total number of fruits at first
= 36 ÷ ¹₃
= 36 x 3
= 108

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

9 p = 108

1 p = 108 ÷ 9 = 12

Number of lemons that Yen had at first
= 3 p
= 3 x 12
= 36

Answer(s): 36