Lynn had some fruits at her stall. ³₈ of them were oranges, ¹₃ of the remainder were dragon fruits and the rest were apples. The amounts earned for each orange, each dragon fruit and each apple sold are $1.30, $1.10 and $1.70 respectively. The number of oranges sold to the number of dragon fruits sold to the number of apples sold was 5 : 2 : 5. In total, she sold ¹₄ of the fruits and earned $120.40. How many oranges did she have at first?

Oranges	Dragon Fruits	Apples	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of dragon fruits and apples is repeated.  Make the total number of dragon fruits and apples the same. LCM of 5 and 3 is 15.

	Oranges	Dragon Fruits	Apples
Number	5 u	2 u	5 u
Value	$1.30	$1.10	$1.70
Total value	6.5 u	2.2 u	8.5 u

Total amount that Lynn earned
= 6.5 u + 2.2 u + 8.5 u
= 17.2 u

17.2 u = 120.40
 
1 u = 120.40 ÷ 17.2 = 7

Total number of fruits sold
= 5 u + 2 u + 5 u
= 12 u
= 12 x 7
= 84

Total number of fruits at first
= 84 ÷ ¹₄
= 84 x 4
= 336

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

24 p = 336

1 p = 336 ÷ 24 = 14

Number of oranges that Lynn had at first
= 9 p
= 9 x 14
= 126

Answer(s): 126