Tiffany had some fruits at her stall. ¹₃ of them were apricots, ¹₄ of the remainder were pomegranates and the rest were apples. The amounts earned for each apricot, each pomegranate and each apple sold are $1.90, $1.30 and $1.80 respectively. The number of apricots sold to the number of pomegranates sold to the number of apples sold was 5 : 5 : 3. In total, she sold ¹₂ of the fruits and earned $256.80. How many apricots did she have at first?

Apricots	Pomegranates	Apples	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of pomegranates and apples is repeated.  Make the total number of pomegranates and apples the same. LCM of 2 and 4 is 4.

	Apricots	Pomegranates	Apples
Number	5 u	5 u	3 u
Value	$1.90	$1.30	$1.80
Total value	9.5 u	6.5 u	5.4 u

Total amount that Tiffany earned
= 9.5 u + 6.5 u + 5.4 u
= 21.4 u

21.4 u = 256.80
 
1 u = 256.80 ÷ 21.4 = 12

Total number of fruits sold
= 5 u + 5 u + 3 u
= 13 u
= 13 x 12
= 156

Total number of fruits at first
= 156 ÷ ¹₂
= 156 x 2
= 312

Total number of fruits at first
= 2 p + 1 p + 3 p
= 6 p

6 p = 312

1 p = 312 ÷ 6 = 52

Number of apricots that Tiffany had at first
= 2 p
= 2 x 52
= 104

Answer(s): 104