Xandra had some fruits at her stall. ¹₃ of them were apricots, ³₄ of the remainder were guavas and the rest were pears. The amounts earned for each apricot, each guava and each pear sold are $1.10, $1.20 and $1.70 respectively. The number of apricots sold to the number of guavas sold to the number of pears sold was 4 : 3 : 2. In total, she sold ¹₂ of the fruits and earned $34.20. How many apricots did she have at first?

Apricots	Guavas	Pears	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of guavas and pears is repeated.  Make the total number of guavas and pears the same. LCM of 2 and 4 is 4.

	Apricots	Guavas	Pears
Number	4 u	3 u	2 u
Value	$1.10	$1.20	$1.70
Total value	4.4 u	3.6 u	3.4 u

Total amount that Xandra earned
= 4.4 u + 3.6 u + 3.4 u
= 11.4 u

11.4 u = 34.20
 
1 u = 34.20 ÷ 11.4 = 3

Total number of fruits sold
= 4 u + 3 u + 2 u
= 9 u
= 9 x 3
= 27

Total number of fruits at first
= 27 ÷ ¹₂
= 27 x 2
= 54

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

6 p = 54

1 p = 54 ÷ 6 = 9

Number of apricots that Xandra had at first
= 2 p
= 2 x 9
= 18

Answer(s): 18