Shannon had some fruits at her stall. ³₈ of them were peaches, ³₄ of the remainder were pomegranates and the rest were guavas. The amounts earned for each peach, each pomegranate and each guava sold are $1.10, $1.20 and $1.70 respectively. The number of peaches sold to the number of pomegranates sold to the number of guavas sold was 5 : 3 : 4. In total, she sold ¹₁₆ of the fruits and earned $190.80. How many guavas did she have at first?

Peaches	Pomegranates	Guavas	Total
3x4	5x4		8x4
	3x5	1x5
12 p	15 p	5 p	32 p

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

	Peaches	Pomegranates	Guavas
Number	5 u	3 u	4 u
Value	$1.10	$1.20	$1.70
Total value	5.5 u	3.6 u	6.8 u

Total amount that Shannon earned
= 5.5 u + 3.6 u + 6.8 u
= 15.9 u

15.9 u = 190.80
 
1 u = 190.80 ÷ 15.9 = 12

Total number of fruits sold
= 5 u + 3 u + 4 u
= 12 u
= 12 x 12
= 144

Total number of fruits at first
= 144 ÷ ¹₁₆
= 144 x 16
= 2304

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

32 p = 2304

1 p = 2304 ÷ 32 = 72

Number of guavas that Shannon had at first
= 5 p
= 5 x 72
= 360

Answer(s): 360