Dana had some fruits at her stall. ¹₃ of them were kiwis, ¹₄ of the remainder were tomatoes and the rest were guavas. The amounts earned for each kiwi, each tomato and each guava sold are $1.90, $1.40 and $1.70 respectively. The number of kiwis sold to the number of tomatoes sold to the number of guavas sold was 5 : 1 : 2. In total, she sold ¹₃ of the fruits and earned $100.10. How many guavas did she have at first?

Kiwis	Tomatoes	Guavas	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of tomatoes and guavas is repeated.  Make the total number of tomatoes and guavas the same. LCM of 2 and 4 is 4.

	Kiwis	Tomatoes	Guavas
Number	5 u	1 u	2 u
Value	$1.90	$1.40	$1.70
Total value	9.5 u	1.4 u	3.4 u

Total amount that Dana earned
= 9.5 u + 1.4 u + 3.4 u
= 14.3 u

14.3 u = 100.10
 
1 u = 100.10 ÷ 14.3 = 7

Total number of fruits sold
= 5 u + 1 u + 2 u
= 8 u
= 8 x 7
= 56

Total number of fruits at first
= 56 ÷ ¹₃
= 56 x 3
= 168

Total number of fruits at first
= 2 p + 1 p + 3 p
= 6 p

6 p = 168

1 p = 168 ÷ 6 = 28

Number of guavas that Dana had at first
= 3 p
= 3 x 28
= 84

Answer(s): 84