Roshel had some fruits at her stall. ³₈ of them were limes, ¹₄ of the remainder were peaches and the rest were mandarin oranges. The amounts earned for each lime, each peach and each mandarin orange sold are $1.90, $1.50 and $1.40 respectively. The number of limes sold to the number of peaches sold to the number of mandarin oranges sold was 5 : 5 : 4. In total, she sold ¹₁₆ of the fruits and earned $158.20. How many mandarin oranges did she have at first?

Limes	Peaches	Mandarin Oranges	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

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

	Limes	Peaches	Mandarin Oranges
Number	5 u	5 u	4 u
Value	$1.90	$1.50	$1.40
Total value	9.5 u	7.5 u	5.6 u

Total amount that Roshel earned
= 9.5 u + 7.5 u + 5.6 u
= 22.6 u

22.6 u = 158.20
 
1 u = 158.20 ÷ 22.6 = 7

Total number of fruits sold
= 5 u + 5 u + 4 u
= 14 u
= 14 x 7
= 98

Total number of fruits at first
= 98 ÷ ¹₁₆
= 98 x 16
= 1568

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

32 p = 1568

1 p = 1568 ÷ 32 = 49

Number of mandarin oranges that Roshel had at first
= 15 p
= 15 x 49
= 735

Answer(s): 735