Vanessa had some fruits at her stall. ³₈ of them were dates, ²₃ of the remainder were limes and the rest were dragon fruits. The amounts earned for each date, each lime and each dragon fruit sold are $1.20, $1.90 and $1.60 respectively. The number of dates sold to the number of limes sold to the number of dragon fruits sold was 3 : 5 : 1. In total, she sold ¹₈ of the fruits and earned $88.20. How many dates did she have at first?

Dates	Limes	Dragon Fruits	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of limes and dragon fruits is repeated.  Make the total number of limes and dragon fruits the same. LCM of 5 and 3 is 15.

	Dates	Limes	Dragon Fruits
Number	3 u	5 u	1 u
Value	$1.20	$1.90	$1.60
Total value	3.6 u	9.5 u	1.6 u

Total amount that Vanessa earned
= 3.6 u + 9.5 u + 1.6 u
= 14.7 u

14.7 u = 88.20
 
1 u = 88.20 ÷ 14.7 = 6

Total number of fruits sold
= 3 u + 5 u + 1 u
= 9 u
= 9 x 6
= 54

Total number of fruits at first
= 54 ÷ ¹₈
= 54 x 8
= 432

Total number of fruits at first
= 9 p + 10 p + 5 p
= 24 p

24 p = 432

1 p = 432 ÷ 24 = 18

Number of dates that Vanessa had at first
= 9 p
= 9 x 18
= 162

Answer(s): 162