Opal had some fruits at her stall. ³₈ of them were tomatoes, ¹₄ of the remainder were kiwis and the rest were guavas. The amounts earned for each tomato, each kiwi and each guava sold are $1.30, $1.80 and $1.50 respectively. The number of tomatoes sold to the number of kiwis sold to the number of guavas sold was 5 : 4 : 5. In total, she sold ¹₁₆ of the fruits and earned $381.60. How many tomatoes did she have at first?

Tomatoes	Kiwis	Guavas	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of kiwis and guavas is repeated.  Make the total number of kiwis and guavas the same. LCM of 5 and 4 is 20.

	Tomatoes	Kiwis	Guavas
Number	5 u	4 u	5 u
Value	$1.30	$1.80	$1.50
Total value	6.5 u	7.2 u	7.5 u

Total amount that Opal earned
= 6.5 u + 7.2 u + 7.5 u
= 21.2 u

21.2 u = 381.60
 
1 u = 381.60 ÷ 21.2 = 18

Total number of fruits sold
= 5 u + 4 u + 5 u
= 14 u
= 14 x 18
= 252

Total number of fruits at first
= 252 ÷ ¹₁₆
= 252 x 16
= 4032

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

32 p = 4032

1 p = 4032 ÷ 32 = 126

Number of tomatoes that Opal had at first
= 12 p
= 12 x 126
= 1512

Answer(s): 1512