Jen had some fruits at her stall. ¹₃ of them were apricots, ¹₅ of the remainder were oranges and the rest were limes. The amounts earned for each apricot, each orange and each lime sold are $1.70, $1.40 and $1.60 respectively. The number of apricots sold to the number of oranges sold to the number of limes sold was 1 : 1 : 3. In total, she sold ¹₃ of the fruits and earned $71.10. How many limes did she have at first?

Apricots	Oranges	Limes	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of oranges and limes is repeated.  Make the total number of oranges and limes the same. LCM of 2 and 5 is 10.

	Apricots	Oranges	Limes
Number	1 u	1 u	3 u
Value	$1.70	$1.40	$1.60
Total value	1.7 u	1.4 u	4.8 u

Total amount that Jen earned
= 1.7 u + 1.4 u + 4.8 u
= 7.9 u

7.9 u = 71.10
 
1 u = 71.10 ÷ 7.9 = 9

Total number of fruits sold
= 1 u + 1 u + 3 u
= 5 u
= 5 x 9
= 45

Total number of fruits at first
= 45 ÷ ¹₃
= 45 x 3
= 135

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 135

1 p = 135 ÷ 15 = 9

Number of limes that Jen had at first
= 8 p
= 8 x 9
= 72

Answer(s): 72