Elyse had some fruits at her stall. ¹₃ of them were avocados, ¹₃ of the remainder were plums and the rest were papayas. The amounts earned for each avocado, each plum and each papaya sold are $1.70, $1.10 and $1.90 respectively. The number of avocados sold to the number of plums sold to the number of papayas sold was 1 : 3 : 3. In total, she sold ¹₃ of the fruits and earned $160.50. How many papayas did she have at first?

Avocados	Plums	Papayas	Total
1x3	2x3		3x3
	1x2	2x2
3 p	2 p	4 p	9 p

The total number of plums and papayas is repeated.  Make the total number of plums and papayas the same. LCM of 2 and 3 is 6.

	Avocados	Plums	Papayas
Number	1 u	3 u	3 u
Value	$1.70	$1.10	$1.90
Total value	1.7 u	3.3 u	5.7 u

Total amount that Elyse earned
= 1.7 u + 3.3 u + 5.7 u
= 10.7 u

10.7 u = 160.50
 
1 u = 160.50 ÷ 10.7 = 15

Total number of fruits sold
= 1 u + 3 u + 3 u
= 7 u
= 7 x 15
= 105

Total number of fruits at first
= 105 ÷ ¹₃
= 105 x 3
= 315

Total number of fruits at first
= 3 p + 2 p + 4 p
= 9 p

9 p = 315

1 p = 315 ÷ 9 = 35

Number of papayas that Elyse had at first
= 4 p
= 4 x 35
= 140

Answer(s): 140