Joelle had some fruits at her stall. ³₈ of them were pomegranates, ¹₂ of the remainder were grapefruits and the rest were oranges. The amounts earned for each pomegranate, each grapefruit and each orange sold are $1.30, $1.60 and $1.50 respectively. The number of pomegranates sold to the number of grapefruits sold to the number of oranges sold was 4 : 3 : 3. In total, she sold ¹₈ of the fruits and earned $101.50. How many pomegranates did she have at first?

Pomegranates	Grapefruits	Oranges	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of grapefruits and oranges is repeated.  Make the total number of grapefruits and oranges the same. LCM of 5 and 2 is 10.

	Pomegranates	Grapefruits	Oranges
Number	4 u	3 u	3 u
Value	$1.30	$1.60	$1.50
Total value	5.2 u	4.8 u	4.5 u

Total amount that Joelle earned
= 5.2 u + 4.8 u + 4.5 u
= 14.5 u

14.5 u = 101.50
 
1 u = 101.50 ÷ 14.5 = 7

Total number of fruits sold
= 4 u + 3 u + 3 u
= 10 u
= 10 x 7
= 70

Total number of fruits at first
= 70 ÷ ¹₈
= 70 x 8
= 560

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 560

1 p = 560 ÷ 16 = 35

Number of pomegranates that Joelle had at first
= 6 p
= 6 x 35
= 210

Answer(s): 210