Usha had some fruits at her stall. ³₈ of them were tomatoes, ¹₃ of the remainder were avocados and the rest were dates. The amounts earned for each tomato, each avocado and each date sold are $1.40, $1.10 and $1.70 respectively. The number of tomatoes sold to the number of avocados sold to the number of dates sold was 4 : 3 : 2. In total, she sold ¹₈ of the fruits and earned $233.70. How many dates did she have at first?

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

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

	Tomatoes	Avocados	Dates
Number	4 u	3 u	2 u
Value	$1.40	$1.10	$1.70
Total value	5.6 u	3.3 u	3.4 u

Total amount that Usha earned
= 5.6 u + 3.3 u + 3.4 u
= 12.3 u

12.3 u = 233.70
 
1 u = 233.70 ÷ 12.3 = 19

Total number of fruits sold
= 4 u + 3 u + 2 u
= 9 u
= 9 x 19
= 171

Total number of fruits at first
= 171 ÷ ¹₈
= 171 x 8
= 1368

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

24 p = 1368

1 p = 1368 ÷ 24 = 57

Number of dates that Usha had at first
= 10 p
= 10 x 57
= 570

Answer(s): 570