Xandra had some fruits at her stall. ¹₃ of them were peaches, ³₄ of the remainder were papayas and the rest were pears. The amounts earned for each peach, each papaya and each pear sold are $1.70, $1.10 and $1.50 respectively. The number of peaches sold to the number of papayas sold to the number of pears sold was 2 : 4 : 3. In total, she sold ¹₃ of the fruits and earned $172.20. How many peaches did she have at first?

Peaches	Papayas	Pears	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of papayas and pears is repeated.  Make the total number of papayas and pears the same. LCM of 2 and 4 is 4.

	Peaches	Papayas	Pears
Number	2 u	4 u	3 u
Value	$1.70	$1.10	$1.50
Total value	3.4 u	4.4 u	4.5 u

Total amount that Xandra earned
= 3.4 u + 4.4 u + 4.5 u
= 12.3 u

12.3 u = 172.20
 
1 u = 172.20 ÷ 12.3 = 14

Total number of fruits sold
= 2 u + 4 u + 3 u
= 9 u
= 9 x 14
= 126

Total number of fruits at first
= 126 ÷ ¹₃
= 126 x 3
= 378

Total number of fruits at first
= 2 p + 3 p + 1 p
= 6 p

6 p = 378

1 p = 378 ÷ 6 = 63

Number of peaches that Xandra had at first
= 2 p
= 2 x 63
= 126

Answer(s): 126