Raeann had some fruits at her stall. ¹₃ of them were pears, ¹₃ of the remainder were mandarin oranges and the rest were lemons. The amounts earned for each pear, each mandarin orange and each lemon sold are $1.10, $1.20 and $1.40 respectively. The number of pears sold to the number of mandarin oranges sold to the number of lemons sold was 1 : 4 : 4. In total, she sold ¹₃ of the fruits and earned $126.50. How many lemons did she have at first?

Pears	Mandarin Oranges	Lemons	Total
1x3	2x3		3x3
	1x2	2x2
3 p	2 p	4 p	9 p

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

	Pears	Mandarin Oranges	Lemons
Number	1 u	4 u	4 u
Value	$1.10	$1.20	$1.40
Total value	1.1 u	4.8 u	5.6 u

Total amount that Raeann earned
= 1.1 u + 4.8 u + 5.6 u
= 11.5 u

11.5 u = 126.50
 
1 u = 126.50 ÷ 11.5 = 11

Total number of fruits sold
= 1 u + 4 u + 4 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 + 2 p + 4 p
= 9 p

9 p = 297

1 p = 297 ÷ 9 = 33

Number of lemons that Raeann had at first
= 4 p
= 4 x 33
= 132

Answer(s): 132