Lucy had some fruits at her stall. ³₈ of them were dates, ²₃ of the remainder were avocados and the rest were apples. The amounts earned for each date, each avocado and each apple sold are $1.40, $1.90 and $1.70 respectively. The number of dates sold to the number of avocados sold to the number of apples sold was 1 : 1 : 4. In total, she sold ¹₈ of the fruits and earned $111.10. How many dates did she have at first?

Dates	Avocados	Apples	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of avocados and apples is repeated.  Make the total number of avocados and apples the same. LCM of 5 and 3 is 15.

	Dates	Avocados	Apples
Number	1 u	1 u	4 u
Value	$1.40	$1.90	$1.70
Total value	1.4 u	1.9 u	6.8 u

Total amount that Lucy earned
= 1.4 u + 1.9 u + 6.8 u
= 10.1 u

10.1 u = 111.10
 
1 u = 111.10 ÷ 10.1 = 11

Total number of fruits sold
= 1 u + 1 u + 4 u
= 6 u
= 6 x 11
= 66

Total number of fruits at first
= 66 ÷ ¹₈
= 66 x 8
= 528

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

24 p = 528

1 p = 528 ÷ 24 = 22

Number of dates that Lucy had at first
= 9 p
= 9 x 22
= 198

Answer(s): 198