Gem had some fruits at her stall. ³₈ of them were oranges, ²₃ of the remainder were papayas and the rest were tomatoes. The amounts earned for each orange, each papaya and each tomato sold are $1.70, $1.40 and $1.60 respectively. The number of oranges sold to the number of papayas sold to the number of tomatoes sold was 2 : 3 : 3. In total, she sold ¹₆ of the fruits and earned $198.40. How many tomatoes did she have at first?

Oranges	Papayas	Tomatoes	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

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

	Oranges	Papayas	Tomatoes
Number	2 u	3 u	3 u
Value	$1.70	$1.40	$1.60
Total value	3.4 u	4.2 u	4.8 u

Total amount that Gem earned
= 3.4 u + 4.2 u + 4.8 u
= 12.4 u

12.4 u = 198.40
 
1 u = 198.40 ÷ 12.4 = 16

Total number of fruits sold
= 2 u + 3 u + 3 u
= 8 u
= 8 x 16
= 128

Total number of fruits at first
= 128 ÷ ¹₆
= 128 x 6
= 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 Gem had at first
= 5 p
= 5 x 32
= 160

Answer(s): 160