Jean had some fruits at her stall. ³₈ of them were apples, ²₃ of the remainder were dates and the rest were tomatoes. The amounts earned for each apple, each date and each tomato sold are $1.10, $1.60 and $1.70 respectively. The number of apples sold to the number of dates sold to the number of tomatoes sold was 5 : 3 : 4. In total, she sold ¹₄ of the fruits and earned $273.60. How many tomatoes did she have at first?

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

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

	Apples	Dates	Tomatoes
Number	5 u	3 u	4 u
Value	$1.10	$1.60	$1.70
Total value	5.5 u	4.8 u	6.8 u

Total amount that Jean earned
= 5.5 u + 4.8 u + 6.8 u
= 17.1 u

17.1 u = 273.60
 
1 u = 273.60 ÷ 17.1 = 16

Total number of fruits sold
= 5 u + 3 u + 4 u
= 12 u
= 12 x 16
= 192

Total number of fruits at first
= 192 ÷ ¹₄
= 192 x 4
= 768

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

24 p = 768

1 p = 768 ÷ 24 = 32

Number of tomatoes that Jean had at first
= 5 p
= 5 x 32
= 160

Answer(s): 160