Wendy had some fruits at her stall. ³₈ of them were papayas, ²₃ of the remainder were guavas and the rest were dates. The amounts earned for each papaya, each guava and each date sold are $1.80, $1.30 and $1.70 respectively. The number of papayas sold to the number of guavas sold to the number of dates sold was 1 : 1 : 2. In total, she sold ¹₄ of the fruits and earned $97.50. How many dates did she have at first?

Papayas	Guavas	Dates	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

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

	Papayas	Guavas	Dates
Number	1 u	1 u	2 u
Value	$1.80	$1.30	$1.70
Total value	1.8 u	1.3 u	3.4 u

Total amount that Wendy earned
= 1.8 u + 1.3 u + 3.4 u
= 6.5 u

6.5 u = 97.50
 
1 u = 97.50 ÷ 6.5 = 15

Total number of fruits sold
= 1 u + 1 u + 2 u
= 4 u
= 4 x 15
= 60

Total number of fruits at first
= 60 ÷ ¹₄
= 60 x 4
= 240

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

24 p = 240

1 p = 240 ÷ 24 = 10

Number of dates that Wendy had at first
= 5 p
= 5 x 10
= 50

Answer(s): 50