Esther had some fruits at her stall. ³₈ of them were avocados, ¹₃ of the remainder were peaches and the rest were grapefruits. The amounts earned for each avocado, each peach and each grapefruit sold are $1.30, $1.60 and $1.40 respectively. The number of avocados sold to the number of peaches sold to the number of grapefruits sold was 1 : 4 : 3. In total, she sold ¹₁₂ of the fruits and earned $154.70. How many avocados did she have at first?

Avocados	Peaches	Grapefruits	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of peaches and grapefruits is repeated.  Make the total number of peaches and grapefruits the same. LCM of 5 and 3 is 15.

	Avocados	Peaches	Grapefruits
Number	1 u	4 u	3 u
Value	$1.30	$1.60	$1.40
Total value	1.3 u	6.4 u	4.2 u

Total amount that Esther earned
= 1.3 u + 6.4 u + 4.2 u
= 11.9 u

11.9 u = 154.70
 
1 u = 154.70 ÷ 11.9 = 13

Total number of fruits sold
= 1 u + 4 u + 3 u
= 8 u
= 8 x 13
= 104

Total number of fruits at first
= 104 ÷ ¹₁₂
= 104 x 12
= 1248

Total number of fruits at first
= 9 p + 5 p + 10 p
= 24 p

24 p = 1248

1 p = 1248 ÷ 24 = 52

Number of avocados that Esther had at first
= 9 p
= 9 x 52
= 468

Answer(s): 468