Cindy had some fruits at her stall. ³₈ of them were apricots, ³₄ of the remainder were avocados and the rest were mandarin oranges. The amounts earned for each apricot, each avocado and each mandarin orange sold are $1.70, $1.60 and $1.20 respectively. The number of apricots sold to the number of avocados sold to the number of mandarin oranges sold was 3 : 4 : 1. In total, she sold ¹₁₆ of the fruits and earned $101.60. How many mandarin oranges did she have at first?

Apricots	Avocados	Mandarin Oranges	Total
3x4	5x4		8x4
	3x5	1x5
12 p	15 p	5 p	32 p

The total number of avocados and mandarin oranges is repeated.  Make the total number of avocados and mandarin oranges the same. LCM of 5 and 4 is 20.

	Apricots	Avocados	Mandarin Oranges
Number	3 u	4 u	1 u
Value	$1.70	$1.60	$1.20
Total value	5.1 u	6.4 u	1.2 u

Total amount that Cindy earned
= 5.1 u + 6.4 u + 1.2 u
= 12.7 u

12.7 u = 101.60
 
1 u = 101.60 ÷ 12.7 = 8

Total number of fruits sold
= 3 u + 4 u + 1 u
= 8 u
= 8 x 8
= 64

Total number of fruits at first
= 64 ÷ ¹₁₆
= 64 x 16
= 1024

Total number of fruits at first
= 12 p + 15 p + 5 p
= 32 p

32 p = 1024

1 p = 1024 ÷ 32 = 32

Number of mandarin oranges that Cindy had at first
= 5 p
= 5 x 32
= 160

Answer(s): 160