Jen had some fruits at her stall. ³₈ of them were kiwis, ¹₄ of the remainder were limes and the rest were lemons. The amounts earned for each kiwi, each lime and each lemon sold are $1.90, $1.60 and $1.10 respectively. The number of kiwis sold to the number of limes sold to the number of lemons sold was 3 : 2 : 5. In total, she sold ¹₁₆ of the fruits and earned $129.60. How many lemons did she have at first?

Kiwis	Limes	Lemons	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of limes and lemons is repeated.  Make the total number of limes and lemons the same. LCM of 5 and 4 is 20.

	Kiwis	Limes	Lemons
Number	3 u	2 u	5 u
Value	$1.90	$1.60	$1.10
Total value	5.7 u	3.2 u	5.5 u

Total amount that Jen earned
= 5.7 u + 3.2 u + 5.5 u
= 14.4 u

14.4 u = 129.60
 
1 u = 129.60 ÷ 14.4 = 9

Total number of fruits sold
= 3 u + 2 u + 5 u
= 10 u
= 10 x 9
= 90

Total number of fruits at first
= 90 ÷ ¹₁₆
= 90 x 16
= 1440

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

32 p = 1440

1 p = 1440 ÷ 32 = 45

Number of lemons that Jen had at first
= 15 p
= 15 x 45
= 675

Answer(s): 675