Shannon had some fruits at her stall. ³₈ of them were kiwis, ¹₃ of the remainder were grapefruits and the rest were lemons. The amounts earned for each kiwi, each grapefruit and each lemon sold are $1.70, $1.20 and $1.90 respectively. The number of kiwis sold to the number of grapefruits sold to the number of lemons sold was 2 : 1 : 3. In total, she sold ¹₄ of the fruits and earned $41.20. How many kiwis did she have at first?

Kiwis	Grapefruits	Lemons	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of grapefruits and lemons is repeated.  Make the total number of grapefruits and lemons the same. LCM of 5 and 3 is 15.

	Kiwis	Grapefruits	Lemons
Number	2 u	1 u	3 u
Value	$1.70	$1.20	$1.90
Total value	3.4 u	1.2 u	5.7 u

Total amount that Shannon earned
= 3.4 u + 1.2 u + 5.7 u
= 10.3 u

10.3 u = 41.20
 
1 u = 41.20 ÷ 10.3 = 4

Total number of fruits sold
= 2 u + 1 u + 3 u
= 6 u
= 6 x 4
= 24

Total number of fruits at first
= 24 ÷ ¹₄
= 24 x 4
= 96

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

24 p = 96

1 p = 96 ÷ 24 = 4

Number of kiwis that Shannon had at first
= 9 p
= 9 x 4
= 36

Answer(s): 36