Penelope had some fruits at her stall. ³₈ of them were apples, ²₃ of the remainder were mangosteens and the rest were kiwis. The amounts earned for each apple, each mangosteen and each kiwi sold are $1.90, $1.20 and $1.40 respectively. The number of apples sold to the number of mangosteens sold to the number of kiwis sold was 1 : 3 : 1. In total, she sold ¹₆ of the fruits and earned $110.40. How many kiwis did she have at first?

Apples	Mangosteens	Kiwis	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of mangosteens and kiwis is repeated.  Make the total number of mangosteens and kiwis the same. LCM of 5 and 3 is 15.

	Apples	Mangosteens	Kiwis
Number	1 u	3 u	1 u
Value	$1.90	$1.20	$1.40
Total value	1.9 u	3.6 u	1.4 u

Total amount that Penelope earned
= 1.9 u + 3.6 u + 1.4 u
= 6.9 u

6.9 u = 110.40
 
1 u = 110.40 ÷ 6.9 = 16

Total number of fruits sold
= 1 u + 3 u + 1 u
= 5 u
= 5 x 16
= 80

Total number of fruits at first
= 80 ÷ ¹₆
= 80 x 6
= 480

Total number of fruits at first
= 9 p + 10 p + 5 p
= 24 p

24 p = 480

1 p = 480 ÷ 24 = 20

Number of kiwis that Penelope had at first
= 5 p
= 5 x 20
= 100

Answer(s): 100