Risa had some fruits at her stall. ³₈ of them were grapefruits, ²₃ of the remainder were mangosteens and the rest were apples. The amounts earned for each grapefruit, each mangosteen and each apple sold are $1.90, $1.10 and $1.70 respectively. The number of grapefruits sold to the number of mangosteens sold to the number of apples sold was 5 : 5 : 3. In total, she sold ¹₁₂ of the fruits and earned $80.40. How many grapefruits did she have at first?

Grapefruits	Mangosteens	Apples	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of mangosteens and apples is repeated.  Make the total number of mangosteens and apples the same. LCM of 5 and 3 is 15.

	Grapefruits	Mangosteens	Apples
Number	5 u	5 u	3 u
Value	$1.90	$1.10	$1.70
Total value	9.5 u	5.5 u	5.1 u

Total amount that Risa earned
= 9.5 u + 5.5 u + 5.1 u
= 20.1 u

20.1 u = 80.40
 
1 u = 80.40 ÷ 20.1 = 4

Total number of fruits sold
= 5 u + 5 u + 3 u
= 13 u
= 13 x 4
= 52

Total number of fruits at first
= 52 ÷ ¹₁₂
= 52 x 12
= 624

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

24 p = 624

1 p = 624 ÷ 24 = 26

Number of grapefruits that Risa had at first
= 9 p
= 9 x 26
= 234

Answer(s): 234