Usha had some fruits at her stall. ³₈ of them were plums, ¹₃ of the remainder were apricots and the rest were mangosteens. The amounts earned for each plum, each apricot and each mangosteen sold are $1.90, $1.40 and $1.50 respectively. The number of plums sold to the number of apricots sold to the number of mangosteens sold was 5 : 1 : 3. In total, she sold ¹₈ of the fruits and earned $46.20. How many plums did she have at first?

Plums	Apricots	Mangosteens	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of apricots and mangosteens is repeated.  Make the total number of apricots and mangosteens the same. LCM of 5 and 3 is 15.

	Plums	Apricots	Mangosteens
Number	5 u	1 u	3 u
Value	$1.90	$1.40	$1.50
Total value	9.5 u	1.4 u	4.5 u

Total amount that Usha earned
= 9.5 u + 1.4 u + 4.5 u
= 15.4 u

15.4 u = 46.20
 
1 u = 46.20 ÷ 15.4 = 3

Total number of fruits sold
= 5 u + 1 u + 3 u
= 9 u
= 9 x 3
= 27

Total number of fruits at first
= 27 ÷ ¹₈
= 27 x 8
= 216

Total number of fruits at first
= 9 p + 5 p + 10 p
= 24 p

24 p = 216

1 p = 216 ÷ 24 = 9

Number of plums that Usha had at first
= 9 p
= 9 x 9
= 81

Answer(s): 81