Rachel had some fruits at her stall. ³₈ of them were coconuts, ³₄ of the remainder were guavas and the rest were dates. The amounts earned for each coconut, each guava and each date sold are $1.60, $1.30 and $1.10 respectively. The number of coconuts sold to the number of guavas sold to the number of dates sold was 3 : 1 : 1. In total, she sold ¹₈ of the fruits and earned $86.40. How many coconuts did she have at first?

Coconuts	Guavas	Dates	Total
3x4	5x4		8x4
	3x5	1x5
12 p	15 p	5 p	32 p

The total number of guavas and dates is repeated.  Make the total number of guavas and dates the same. LCM of 5 and 4 is 20.

	Coconuts	Guavas	Dates
Number	3 u	1 u	1 u
Value	$1.60	$1.30	$1.10
Total value	4.8 u	1.3 u	1.1 u

Total amount that Rachel earned
= 4.8 u + 1.3 u + 1.1 u
= 7.2 u

7.2 u = 86.40
 
1 u = 86.40 ÷ 7.2 = 12

Total number of fruits sold
= 3 u + 1 u + 1 u
= 5 u
= 5 x 12
= 60

Total number of fruits at first
= 60 ÷ ¹₈
= 60 x 8
= 480

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

32 p = 480

1 p = 480 ÷ 32 = 15

Number of coconuts that Rachel had at first
= 12 p
= 12 x 15
= 180

Answer(s): 180