Zara had some fruits at her stall. ³₈ of them were dragon fruits, ¹₄ of the remainder were peaches and the rest were plums. The amounts earned for each dragon fruit, each peach and each plum sold are $1.70, $1.30 and $1.20 respectively. The number of dragon fruits sold to the number of peaches sold to the number of plums sold was 3 : 5 : 1. In total, she sold ¹₈ of the fruits and earned $153.60. How many plums did she have at first?

Dragon Fruits	Peaches	Plums	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of peaches and plums is repeated.  Make the total number of peaches and plums the same. LCM of 5 and 4 is 20.

	Dragon Fruits	Peaches	Plums
Number	3 u	5 u	1 u
Value	$1.70	$1.30	$1.20
Total value	5.1 u	6.5 u	1.2 u

Total amount that Zara earned
= 5.1 u + 6.5 u + 1.2 u
= 12.8 u

12.8 u = 153.60
 
1 u = 153.60 ÷ 12.8 = 12

Total number of fruits sold
= 3 u + 5 u + 1 u
= 9 u
= 9 x 12
= 108

Total number of fruits at first
= 108 ÷ ¹₈
= 108 x 8
= 864

Total number of fruits at first
= 12 p + 5 p + 15 p
= 32 p

32 p = 864

1 p = 864 ÷ 32 = 27

Number of plums that Zara had at first
= 15 p
= 15 x 27
= 405

Answer(s): 405