Mary had some fruits at her stall. ³₈ of them were avocados, ²₃ of the remainder were oranges and the rest were mandarin oranges. The amounts earned for each avocado, each orange and each mandarin orange sold are $1.50, $1.10 and $1.70 respectively. The number of avocados sold to the number of oranges sold to the number of mandarin oranges sold was 5 : 3 : 4. In total, she sold ¹₆ of the fruits and earned $70.40. How many mandarin oranges did she have at first?

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

The total number of oranges and mandarin oranges is repeated.  Make the total number of oranges and mandarin oranges the same. LCM of 5 and 3 is 15.

	Avocados	Oranges	Mandarin Oranges
Number	5 u	3 u	4 u
Value	$1.50	$1.10	$1.70
Total value	7.5 u	3.3 u	6.8 u

Total amount that Mary earned
= 7.5 u + 3.3 u + 6.8 u
= 17.6 u

17.6 u = 70.40
 
1 u = 70.40 ÷ 17.6 = 4

Total number of fruits sold
= 5 u + 3 u + 4 u
= 12 u
= 12 x 4
= 48

Total number of fruits at first
= 48 ÷ ¹₆
= 48 x 6
= 288

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

24 p = 288

1 p = 288 ÷ 24 = 12

Number of mandarin oranges that Mary had at first
= 5 p
= 5 x 12
= 60

Answer(s): 60