Marion had some fruits at her stall. ³₈ of them were apples, ¹₄ of the remainder were guavas and the rest were papayas. The amounts earned for each apple, each guava and each papaya sold are $1.10, $1.20 and $1.40 respectively. The number of apples sold to the number of guavas sold to the number of papayas sold was 1 : 1 : 2. In total, she sold ¹₈ of the fruits and earned $81.60. How many apples did she have at first?

Apples	Guavas	Papayas	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

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

	Apples	Guavas	Papayas
Number	1 u	1 u	2 u
Value	$1.10	$1.20	$1.40
Total value	1.1 u	1.2 u	2.8 u

Total amount that Marion earned
= 1.1 u + 1.2 u + 2.8 u
= 5.1 u

5.1 u = 81.60
 
1 u = 81.60 ÷ 5.1 = 16

Total number of fruits sold
= 1 u + 1 u + 2 u
= 4 u
= 4 x 16
= 64

Total number of fruits at first
= 64 ÷ ¹₈
= 64 x 8
= 512

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

32 p = 512

1 p = 512 ÷ 32 = 16

Number of apples that Marion had at first
= 12 p
= 12 x 16
= 192

Answer(s): 192