Opal had some fruits at her stall. ³₈ of them were pomegranates, ³₄ of the remainder were pears and the rest were tomatoes. The amounts earned for each pomegranate, each pear and each tomato sold are $1.30, $1.10 and $1.80 respectively. The number of pomegranates sold to the number of pears sold to the number of tomatoes sold was 1 : 2 : 2. In total, she sold ¹₁₆ of the fruits and earned $85.20. How many pomegranates did she have at first?

Pomegranates	Pears	Tomatoes	Total
3x4	5x4		8x4
	3x5	1x5
12 p	15 p	5 p	32 p

The total number of pears and tomatoes is repeated.  Make the total number of pears and tomatoes the same. LCM of 5 and 4 is 20.

	Pomegranates	Pears	Tomatoes
Number	1 u	2 u	2 u
Value	$1.30	$1.10	$1.80
Total value	1.3 u	2.2 u	3.6 u

Total amount that Opal earned
= 1.3 u + 2.2 u + 3.6 u
= 7.1 u

7.1 u = 85.20
 
1 u = 85.20 ÷ 7.1 = 12

Total number of fruits sold
= 1 u + 2 u + 2 u
= 5 u
= 5 x 12
= 60

Total number of fruits at first
= 60 ÷ ¹₁₆
= 60 x 16
= 960

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

32 p = 960

1 p = 960 ÷ 32 = 30

Number of pomegranates that Opal had at first
= 12 p
= 12 x 30
= 360

Answer(s): 360