Usha had some fruits at her stall. ¹₃ of them were mandarin oranges, ¹₄ of the remainder were dragon fruits and the rest were coconuts. The amounts earned for each mandarin orange, each dragon fruit and each coconut sold are $1.90, $1.40 and $1.80 respectively. The number of mandarin oranges sold to the number of dragon fruits sold to the number of coconuts sold was 2 : 4 : 3. In total, she sold ¹₃ of the fruits and earned $207.20. How many coconuts did she have at first?

Mandarin Oranges	Dragon Fruits	Coconuts	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of dragon fruits and coconuts is repeated.  Make the total number of dragon fruits and coconuts the same. LCM of 2 and 4 is 4.

	Mandarin Oranges	Dragon Fruits	Coconuts
Number	2 u	4 u	3 u
Value	$1.90	$1.40	$1.80
Total value	3.8 u	5.6 u	5.4 u

Total amount that Usha earned
= 3.8 u + 5.6 u + 5.4 u
= 14.8 u

14.8 u = 207.20
 
1 u = 207.20 ÷ 14.8 = 14

Total number of fruits sold
= 2 u + 4 u + 3 u
= 9 u
= 9 x 14
= 126

Total number of fruits at first
= 126 ÷ ¹₃
= 126 x 3
= 378

Total number of fruits at first
= 2 p + 1 p + 3 p
= 6 p

6 p = 378

1 p = 378 ÷ 6 = 63

Number of coconuts that Usha had at first
= 3 p
= 3 x 63
= 189

Answer(s): 189