Fiona had some fruits at her stall. ¹₃ of them were dragon fruits, ²₃ of the remainder were peaches and the rest were apricots. The amounts earned for each dragon fruit, each peach and each apricot sold are $1.40, $1.70 and $1.30 respectively. The number of dragon fruits sold to the number of peaches sold to the number of apricots sold was 3 : 1 : 3. In total, she sold ¹₃ of the fruits and earned $176.40. How many dragon fruits did she have at first?

Dragon Fruits	Peaches	Apricots	Total
1x3	2x3		3x3
	2x2	1x2
3 p	4 p	2 p	9 p

The total number of peaches and apricots is repeated.  Make the total number of peaches and apricots the same. LCM of 2 and 3 is 6.

	Dragon Fruits	Peaches	Apricots
Number	3 u	1 u	3 u
Value	$1.40	$1.70	$1.30
Total value	4.2 u	1.7 u	3.9 u

Total amount that Fiona earned
= 4.2 u + 1.7 u + 3.9 u
= 9.8 u

9.8 u = 176.40
 
1 u = 176.40 ÷ 9.8 = 18

Total number of fruits sold
= 3 u + 1 u + 3 u
= 7 u
= 7 x 18
= 126

Total number of fruits at first
= 126 ÷ ¹₃
= 126 x 3
= 378

Total number of fruits at first
= 3 p + 4 p + 2 p
= 9 p

9 p = 378

1 p = 378 ÷ 9 = 42

Number of dragon fruits that Fiona had at first
= 3 p
= 3 x 42
= 126

Answer(s): 126