Shannon had some fruits at her stall. ³₈ of them were kiwis, ¹₃ of the remainder were grapefruits and the rest were mandarin oranges. The amounts earned for each kiwi, each grapefruit and each mandarin orange sold are $1.30, $1.60 and $1.40 respectively. The number of kiwis sold to the number of grapefruits sold to the number of mandarin oranges sold was 5 : 4 : 2. In total, she sold ¹₁₂ of the fruits and earned $251.20. How many kiwis did she have at first?

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

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

	Kiwis	Grapefruits	Mandarin Oranges
Number	5 u	4 u	2 u
Value	$1.30	$1.60	$1.40
Total value	6.5 u	6.4 u	2.8 u

Total amount that Shannon earned
= 6.5 u + 6.4 u + 2.8 u
= 15.7 u

15.7 u = 251.20
 
1 u = 251.20 ÷ 15.7 = 16

Total number of fruits sold
= 5 u + 4 u + 2 u
= 11 u
= 11 x 16
= 176

Total number of fruits at first
= 176 ÷ ¹₁₂
= 176 x 12
= 2112

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

24 p = 2112

1 p = 2112 ÷ 24 = 88

Number of kiwis that Shannon had at first
= 9 p
= 9 x 88
= 792

Answer(s): 792