Lynn had some fruits at her stall. ¹₃ of them were dates, ¹₅ of the remainder were dragon fruits and the rest were tomatoes. The amounts earned for each date, each dragon fruit and each tomato sold are $1.50, $1.30 and $1.70 respectively. The number of dates sold to the number of dragon fruits sold to the number of tomatoes sold was 1 : 5 : 4. In total, she sold ¹₃ of the fruits and earned $88.80. How many tomatoes did she have at first?

Dates	Dragon Fruits	Tomatoes	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of dragon fruits and tomatoes is repeated.  Make the total number of dragon fruits and tomatoes the same. LCM of 2 and 5 is 10.

	Dates	Dragon Fruits	Tomatoes
Number	1 u	5 u	4 u
Value	$1.50	$1.30	$1.70
Total value	1.5 u	6.5 u	6.8 u

Total amount that Lynn earned
= 1.5 u + 6.5 u + 6.8 u
= 14.8 u

14.8 u = 88.80
 
1 u = 88.80 ÷ 14.8 = 6

Total number of fruits sold
= 1 u + 5 u + 4 u
= 10 u
= 10 x 6
= 60

Total number of fruits at first
= 60 ÷ ¹₃
= 60 x 3
= 180

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 180

1 p = 180 ÷ 15 = 12

Number of tomatoes that Lynn had at first
= 8 p
= 8 x 12
= 96

Answer(s): 96