Wendy had some fruits at her stall. ³₈ of them were dates, ¹₃ of the remainder were pomegranates and the rest were peaches. The amounts earned for each date, each pomegranate and each peach sold are $1.20, $1.30 and $1.40 respectively. The number of dates sold to the number of pomegranates sold to the number of peaches sold was 2 : 5 : 1. In total, she sold ¹₆ of the fruits and earned $133.90. How many dates did she have at first?

Dates	Pomegranates	Peaches	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of pomegranates and peaches is repeated.  Make the total number of pomegranates and peaches the same. LCM of 5 and 3 is 15.

	Dates	Pomegranates	Peaches
Number	2 u	5 u	1 u
Value	$1.20	$1.30	$1.40
Total value	2.4 u	6.5 u	1.4 u

Total amount that Wendy earned
= 2.4 u + 6.5 u + 1.4 u
= 10.3 u

10.3 u = 133.90
 
1 u = 133.90 ÷ 10.3 = 13

Total number of fruits sold
= 2 u + 5 u + 1 u
= 8 u
= 8 x 13
= 104

Total number of fruits at first
= 104 ÷ ¹₆
= 104 x 6
= 624

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

24 p = 624

1 p = 624 ÷ 24 = 26

Number of dates that Wendy had at first
= 9 p
= 9 x 26
= 234

Answer(s): 234