Yen had some fruits at her stall. ¹₃ of them were kiwis, ¹₄ of the remainder were guavas and the rest were avocados. The amounts earned for each kiwi, each guava and each avocado sold are $1.20, $1.90 and $1.80 respectively. The number of kiwis sold to the number of guavas sold to the number of avocados sold was 3 : 1 : 2. In total, she sold ¹₃ of the fruits and earned $172.90. How many avocados did she have at first?

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

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

	Kiwis	Guavas	Avocados
Number	3 u	1 u	2 u
Value	$1.20	$1.90	$1.80
Total value	3.6 u	1.9 u	3.6 u

Total amount that Yen earned
= 3.6 u + 1.9 u + 3.6 u
= 9.1 u

9.1 u = 172.90
 
1 u = 172.90 ÷ 9.1 = 19

Total number of fruits sold
= 3 u + 1 u + 2 u
= 6 u
= 6 x 19
= 114

Total number of fruits at first
= 114 ÷ ¹₃
= 114 x 3
= 342

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

6 p = 342

1 p = 342 ÷ 6 = 57

Number of avocados that Yen had at first
= 3 p
= 3 x 57
= 171

Answer(s): 171