Yen had some fruits at her stall. ¹₃ of them were plums, ¹₄ of the remainder were dates and the rest were pears. The amounts earned for each plum, each date and each pear sold are $1.90, $1.40 and $1.70 respectively. The number of plums sold to the number of dates sold to the number of pears sold was 5 : 3 : 3. In total, she sold ¹₃ of the fruits and earned $263.20. How many pears did she have at first?

Plums	Dates	Pears	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

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

	Plums	Dates	Pears
Number	5 u	3 u	3 u
Value	$1.90	$1.40	$1.70
Total value	9.5 u	4.2 u	5.1 u

Total amount that Yen earned
= 9.5 u + 4.2 u + 5.1 u
= 18.8 u

18.8 u = 263.20
 
1 u = 263.20 ÷ 18.8 = 14

Total number of fruits sold
= 5 u + 3 u + 3 u
= 11 u
= 11 x 14
= 154

Total number of fruits at first
= 154 ÷ ¹₃
= 154 x 3
= 462

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

6 p = 462

1 p = 462 ÷ 6 = 77

Number of pears that Yen had at first
= 3 p
= 3 x 77
= 231

Answer(s): 231