Gem had some fruits at her stall. ¹₃ of them were avocados, ¹₅ of the remainder were kiwis and the rest were peaches. The amounts earned for each avocado, each kiwi and each peach sold are $1.10, $1.90 and $1.30 respectively. The number of avocados sold to the number of kiwis sold to the number of peaches sold was 5 : 2 : 2. In total, she sold ¹₃ of the fruits and earned $178.50. How many avocados did she have at first?

Avocados	Kiwis	Peaches	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of kiwis and peaches is repeated.  Make the total number of kiwis and peaches the same. LCM of 2 and 5 is 10.

	Avocados	Kiwis	Peaches
Number	5 u	2 u	2 u
Value	$1.10	$1.90	$1.30
Total value	5.5 u	3.8 u	2.6 u

Total amount that Gem earned
= 5.5 u + 3.8 u + 2.6 u
= 11.9 u

11.9 u = 178.50
 
1 u = 178.50 ÷ 11.9 = 15

Total number of fruits sold
= 5 u + 2 u + 2 u
= 9 u
= 9 x 15
= 135

Total number of fruits at first
= 135 ÷ ¹₃
= 135 x 3
= 405

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 405

1 p = 405 ÷ 15 = 27

Number of avocados that Gem had at first
= 5 p
= 5 x 27
= 135

Answer(s): 135