Lucy had some fruits at her stall. ³₈ of them were limes, ¹₄ of the remainder were papayas and the rest were pears. The amounts earned for each lime, each papaya and each pear sold are $1.10, $1.50 and $1.30 respectively. The number of limes sold to the number of papayas sold to the number of pears sold was 1 : 1 : 2. In total, she sold ¹₁₆ of the fruits and earned $41.60. How many pears did she have at first?

Limes	Papayas	Pears	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of papayas and pears is repeated.  Make the total number of papayas and pears the same. LCM of 5 and 4 is 20.

	Limes	Papayas	Pears
Number	1 u	1 u	2 u
Value	$1.10	$1.50	$1.30
Total value	1.1 u	1.5 u	2.6 u

Total amount that Lucy earned
= 1.1 u + 1.5 u + 2.6 u
= 5.2 u

5.2 u = 41.60
 
1 u = 41.60 ÷ 5.2 = 8

Total number of fruits sold
= 1 u + 1 u + 2 u
= 4 u
= 4 x 8
= 32

Total number of fruits at first
= 32 ÷ ¹₁₆
= 32 x 16
= 512

Total number of fruits at first
= 12 p + 5 p + 15 p
= 32 p

32 p = 512

1 p = 512 ÷ 32 = 16

Number of pears that Lucy had at first
= 15 p
= 15 x 16
= 240

Answer(s): 240