Vanessa had some fruits at her stall. ¹₃ of them were lemons, ¹₄ of the remainder were guavas and the rest were kiwis. The amounts earned for each lemon, each guava and each kiwi sold are $1.10, $1.70 and $1.30 respectively. The number of lemons sold to the number of guavas sold to the number of kiwis sold was 1 : 1 : 3. In total, she sold ¹₂ of the fruits and earned $120.60. How many lemons did she have at first?

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

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

	Lemons	Guavas	Kiwis
Number	1 u	1 u	3 u
Value	$1.10	$1.70	$1.30
Total value	1.1 u	1.7 u	3.9 u

Total amount that Vanessa earned
= 1.1 u + 1.7 u + 3.9 u
= 6.7 u

6.7 u = 120.60
 
1 u = 120.60 ÷ 6.7 = 18

Total number of fruits sold
= 1 u + 1 u + 3 u
= 5 u
= 5 x 18
= 90

Total number of fruits at first
= 90 ÷ ¹₂
= 90 x 2
= 180

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

6 p = 180

1 p = 180 ÷ 6 = 30

Number of lemons that Vanessa had at first
= 2 p
= 2 x 30
= 60

Answer(s): 60