Rachel had some fruits at her stall. ³₈ of them were avocados, ¹₄ of the remainder were apples and the rest were grapefruits. The amounts earned for each avocado, each apple and each grapefruit sold are $1.40, $1.60 and $1.30 respectively. The number of avocados sold to the number of apples sold to the number of grapefruits sold was 2 : 1 : 3. In total, she sold ¹₈ of the fruits and earned $132.80. How many avocados did she have at first?

Avocados	Apples	Grapefruits	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of apples and grapefruits is repeated.  Make the total number of apples and grapefruits the same. LCM of 5 and 4 is 20.

	Avocados	Apples	Grapefruits
Number	2 u	1 u	3 u
Value	$1.40	$1.60	$1.30
Total value	2.8 u	1.6 u	3.9 u

Total amount that Rachel earned
= 2.8 u + 1.6 u + 3.9 u
= 8.3 u

8.3 u = 132.80
 
1 u = 132.80 ÷ 8.3 = 16

Total number of fruits sold
= 2 u + 1 u + 3 u
= 6 u
= 6 x 16
= 96

Total number of fruits at first
= 96 ÷ ¹₈
= 96 x 8
= 768

Total number of fruits at first
= 12 p + 5 p + 15 p
= 32 p

32 p = 768

1 p = 768 ÷ 32 = 24

Number of avocados that Rachel had at first
= 12 p
= 12 x 24
= 288

Answer(s): 288