Lucy had some fruits at her stall. ³₈ of them were limes, ¹₄ of the remainder were apples and the rest were mandarin oranges. The amounts earned for each lime, each apple and each mandarin orange sold are $1.80, $1.60 and $1.70 respectively. The number of limes sold to the number of apples sold to the number of mandarin oranges sold was 2 : 3 : 1. In total, she sold ¹₈ of the fruits and earned $181.80. How many mandarin oranges did she have at first?

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

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

	Limes	Apples	Mandarin Oranges
Number	2 u	3 u	1 u
Value	$1.80	$1.60	$1.70
Total value	3.6 u	4.8 u	1.7 u

Total amount that Lucy earned
= 3.6 u + 4.8 u + 1.7 u
= 10.1 u

10.1 u = 181.80
 
1 u = 181.80 ÷ 10.1 = 18

Total number of fruits sold
= 2 u + 3 u + 1 u
= 6 u
= 6 x 18
= 108

Total number of fruits at first
= 108 ÷ ¹₈
= 108 x 8
= 864

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

32 p = 864

1 p = 864 ÷ 32 = 27

Number of mandarin oranges that Lucy had at first
= 15 p
= 15 x 27
= 405

Answer(s): 405