Lucy had some fruits at her stall. ¹₃ of them were oranges, ¹₅ of the remainder were dates and the rest were dragon fruits. The amounts earned for each orange, each date and each dragon fruit sold are $1.80, $1.40 and $1.60 respectively. The number of oranges sold to the number of dates sold to the number of dragon fruits sold was 4 : 1 : 2. In total, she sold ¹₅ of the fruits and earned $35.40. How many oranges did she have at first?

Oranges	Dates	Dragon Fruits	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of dates and dragon fruits is repeated.  Make the total number of dates and dragon fruits the same. LCM of 2 and 5 is 10.

	Oranges	Dates	Dragon Fruits
Number	4 u	1 u	2 u
Value	$1.80	$1.40	$1.60
Total value	7.2 u	1.4 u	3.2 u

Total amount that Lucy earned
= 7.2 u + 1.4 u + 3.2 u
= 11.8 u

11.8 u = 35.40
 
1 u = 35.40 ÷ 11.8 = 3

Total number of fruits sold
= 4 u + 1 u + 2 u
= 7 u
= 7 x 3
= 21

Total number of fruits at first
= 21 ÷ ¹₅
= 21 x 5
= 105

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 105

1 p = 105 ÷ 15 = 7

Number of oranges that Lucy had at first
= 5 p
= 5 x 7
= 35

Answer(s): 35