Gabby had some fruits at her stall. ³₈ of them were apples, ²₃ of the remainder were dates and the rest were plums. The amounts earned for each apple, each date and each plum sold are $1.50, $1.70 and $1.90 respectively. The number of apples sold to the number of dates sold to the number of plums sold was 5 : 5 : 2. In total, she sold ¹₈ of the fruits and earned $138.60. How many plums did she have at first?

Apples	Dates	Plums	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of dates and plums is repeated.  Make the total number of dates and plums the same. LCM of 5 and 3 is 15.

	Apples	Dates	Plums
Number	5 u	5 u	2 u
Value	$1.50	$1.70	$1.90
Total value	7.5 u	8.5 u	3.8 u

Total amount that Gabby earned
= 7.5 u + 8.5 u + 3.8 u
= 19.8 u

19.8 u = 138.60
 
1 u = 138.60 ÷ 19.8 = 7

Total number of fruits sold
= 5 u + 5 u + 2 u
= 12 u
= 12 x 7
= 84

Total number of fruits at first
= 84 ÷ ¹₈
= 84 x 8
= 672

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

24 p = 672

1 p = 672 ÷ 24 = 28

Number of plums that Gabby had at first
= 5 p
= 5 x 28
= 140

Answer(s): 140