Barbara had some fruits at her stall. ¹₃ of them were guavas, ²₃ of the remainder were oranges and the rest were lemons. The amounts earned for each guava, each orange and each lemon sold are $1.70, $1.20 and $1.10 respectively. The number of guavas sold to the number of oranges sold to the number of lemons sold was 4 : 2 : 3. In total, she sold ¹₃ of the fruits and earned $137.50. How many lemons did she have at first?

Guavas	Oranges	Lemons	Total
1x3	2x3		3x3
	2x2	1x2
3 p	4 p	2 p	9 p

The total number of oranges and lemons is repeated.  Make the total number of oranges and lemons the same. LCM of 2 and 3 is 6.

	Guavas	Oranges	Lemons
Number	4 u	2 u	3 u
Value	$1.70	$1.20	$1.10
Total value	6.8 u	2.4 u	3.3 u

Total amount that Barbara earned
= 6.8 u + 2.4 u + 3.3 u
= 12.5 u

12.5 u = 137.50
 
1 u = 137.50 ÷ 12.5 = 11

Total number of fruits sold
= 4 u + 2 u + 3 u
= 9 u
= 9 x 11
= 99

Total number of fruits at first
= 99 ÷ ¹₃
= 99 x 3
= 297

Total number of fruits at first
= 3 p + 4 p + 2 p
= 9 p

9 p = 297

1 p = 297 ÷ 9 = 33

Number of lemons that Barbara had at first
= 2 p
= 2 x 33
= 66

Answer(s): 66