Xuan had some fruits at her stall. ¹₃ of them were kiwis, ³₄ of the remainder were plums and the rest were avocados. The amounts earned for each kiwi, each plum and each avocado sold are $1.40, $1.60 and $1.90 respectively. The number of kiwis sold to the number of plums sold to the number of avocados sold was 3 : 4 : 5. In total, she sold ¹₃ of the fruits and earned $180.90. How many kiwis did she have at first?

Kiwis	Plums	Avocados	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

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

	Kiwis	Plums	Avocados
Number	3 u	4 u	5 u
Value	$1.40	$1.60	$1.90
Total value	4.2 u	6.4 u	9.5 u

Total amount that Xuan earned
= 4.2 u + 6.4 u + 9.5 u
= 20.1 u

20.1 u = 180.90
 
1 u = 180.90 ÷ 20.1 = 9

Total number of fruits sold
= 3 u + 4 u + 5 u
= 12 u
= 12 x 9
= 108

Total number of fruits at first
= 108 ÷ ¹₃
= 108 x 3
= 324

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

6 p = 324

1 p = 324 ÷ 6 = 54

Number of kiwis that Xuan had at first
= 2 p
= 2 x 54
= 108

Answer(s): 108