Xylia had some fruits at her stall. ³₈ of them were mandarin oranges, ²₃ of the remainder were apples and the rest were apricots. The amounts earned for each mandarin orange, each apple and each apricot sold are $1.10, $1.50 and $1.90 respectively. The number of mandarin oranges sold to the number of apples sold to the number of apricots sold was 1 : 1 : 3. In total, she sold ¹₈ of the fruits and earned $99.60. How many mandarin oranges did she have at first?

Mandarin Oranges	Apples	Apricots	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

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

	Mandarin Oranges	Apples	Apricots
Number	1 u	1 u	3 u
Value	$1.10	$1.50	$1.90
Total value	1.1 u	1.5 u	5.7 u

Total amount that Xylia earned
= 1.1 u + 1.5 u + 5.7 u
= 8.3 u

8.3 u = 99.60
 
1 u = 99.60 ÷ 8.3 = 12

Total number of fruits sold
= 1 u + 1 u + 3 u
= 5 u
= 5 x 12
= 60

Total number of fruits at first
= 60 ÷ ¹₈
= 60 x 8
= 480

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

24 p = 480

1 p = 480 ÷ 24 = 20

Number of mandarin oranges that Xylia had at first
= 9 p
= 9 x 20
= 180

Answer(s): 180