Kathy had some fruits at her stall. ³₈ of them were avocados, ¹₂ of the remainder were pomegranates and the rest were guavas. The amounts earned for each avocado, each pomegranate and each guava sold are $1.30, $1.40 and $1.90 respectively. The number of avocados sold to the number of pomegranates sold to the number of guavas sold was 5 : 3 : 5. In total, she sold ¹₄ of the fruits and earned $323.20. How many guavas did she have at first?

Avocados	Pomegranates	Guavas	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of pomegranates and guavas is repeated.  Make the total number of pomegranates and guavas the same. LCM of 5 and 2 is 10.

	Avocados	Pomegranates	Guavas
Number	5 u	3 u	5 u
Value	$1.30	$1.40	$1.90
Total value	6.5 u	4.2 u	9.5 u

Total amount that Kathy earned
= 6.5 u + 4.2 u + 9.5 u
= 20.2 u

20.2 u = 323.20
 
1 u = 323.20 ÷ 20.2 = 16

Total number of fruits sold
= 5 u + 3 u + 5 u
= 13 u
= 13 x 16
= 208

Total number of fruits at first
= 208 ÷ ¹₄
= 208 x 4
= 832

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 832

1 p = 832 ÷ 16 = 52

Number of guavas that Kathy had at first
= 5 p
= 5 x 52
= 260

Answer(s): 260