Emma had some fruits at her stall. ³₈ of them were peaches, ¹₃ of the remainder were pomegranates and the rest were dates. The amounts earned for each peach, each pomegranate and each date sold are $1.90, $1.40 and $1.60 respectively. The number of peaches sold to the number of pomegranates sold to the number of dates sold was 2 : 3 : 4. In total, she sold ¹₄ of the fruits and earned $57.60. How many peaches did she have at first?

Peaches	Pomegranates	Dates	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Peaches	Pomegranates	Dates
Number	2 u	3 u	4 u
Value	$1.90	$1.40	$1.60
Total value	3.8 u	4.2 u	6.4 u

Total amount that Emma earned
= 3.8 u + 4.2 u + 6.4 u
= 14.4 u

14.4 u = 57.60
 
1 u = 57.60 ÷ 14.4 = 4

Total number of fruits sold
= 2 u + 3 u + 4 u
= 9 u
= 9 x 4
= 36

Total number of fruits at first
= 36 ÷ ¹₄
= 36 x 4
= 144

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

24 p = 144

1 p = 144 ÷ 24 = 6

Number of peaches that Emma had at first
= 9 p
= 9 x 6
= 54

Answer(s): 54