Lynn had some fruits at her stall. ¹₃ of them were pears, ³₄ of the remainder were apples and the rest were dragon fruits. The amounts earned for each pear, each apple and each dragon fruit sold are $1.40, $1.80 and $1.10 respectively. The number of pears sold to the number of apples sold to the number of dragon fruits sold was 4 : 1 : 1. In total, she sold ¹₃ of the fruits and earned $42.50. How many pears did she have at first?

Pears	Apples	Dragon Fruits	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of apples and dragon fruits is repeated.  Make the total number of apples and dragon fruits the same. LCM of 2 and 4 is 4.

	Pears	Apples	Dragon Fruits
Number	4 u	1 u	1 u
Value	$1.40	$1.80	$1.10
Total value	5.6 u	1.8 u	1.1 u

Total amount that Lynn earned
= 5.6 u + 1.8 u + 1.1 u
= 8.5 u

8.5 u = 42.50
 
1 u = 42.50 ÷ 8.5 = 5

Total number of fruits sold
= 4 u + 1 u + 1 u
= 6 u
= 6 x 5
= 30

Total number of fruits at first
= 30 ÷ ¹₃
= 30 x 3
= 90

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

6 p = 90

1 p = 90 ÷ 6 = 15

Number of pears that Lynn had at first
= 2 p
= 2 x 15
= 30

Answer(s): 30