Eva had some fruits at her stall. ³₈ of them were pomegranates, ¹₃ of the remainder were oranges and the rest were grapefruits. The amounts earned for each pomegranate, each orange and each grapefruit sold are $1.50, $1.20 and $1.40 respectively. The number of pomegranates sold to the number of oranges sold to the number of grapefruits sold was 1 : 4 : 4. In total, she sold ¹₁₂ of the fruits and earned $23.80. How many pomegranates did she have at first?

Pomegranates	Oranges	Grapefruits	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Pomegranates	Oranges	Grapefruits
Number	1 u	4 u	4 u
Value	$1.50	$1.20	$1.40
Total value	1.5 u	4.8 u	5.6 u

Total amount that Eva earned
= 1.5 u + 4.8 u + 5.6 u
= 11.9 u

11.9 u = 23.80
 
1 u = 23.80 ÷ 11.9 = 2

Total number of fruits sold
= 1 u + 4 u + 4 u
= 9 u
= 9 x 2
= 18

Total number of fruits at first
= 18 ÷ ¹₁₂
= 18 x 12
= 216

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

24 p = 216

1 p = 216 ÷ 24 = 9

Number of pomegranates that Eva had at first
= 9 p
= 9 x 9
= 81

Answer(s): 81