Tammy had some fruits at her stall. ³₈ of them were pomegranates, ¹₃ of the remainder were guavas and the rest were pears. The amounts earned for each pomegranate, each guava and each pear sold are $1.70, $1.80 and $1.20 respectively. The number of pomegranates sold to the number of guavas sold to the number of pears sold was 1 : 3 : 3. In total, she sold ¹₈ of the fruits and earned $64.20. How many pomegranates did she have at first?

Pomegranates	Guavas	Pears	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of guavas and pears is repeated.  Make the total number of guavas and pears the same. LCM of 5 and 3 is 15.

	Pomegranates	Guavas	Pears
Number	1 u	3 u	3 u
Value	$1.70	$1.80	$1.20
Total value	1.7 u	5.4 u	3.6 u

Total amount that Tammy earned
= 1.7 u + 5.4 u + 3.6 u
= 10.7 u

10.7 u = 64.20
 
1 u = 64.20 ÷ 10.7 = 6

Total number of fruits sold
= 1 u + 3 u + 3 u
= 7 u
= 7 x 6
= 42

Total number of fruits at first
= 42 ÷ ¹₈
= 42 x 8
= 336

Total number of fruits at first
= 9 p + 5 p + 10 p
= 24 p

24 p = 336

1 p = 336 ÷ 24 = 14

Number of pomegranates that Tammy had at first
= 9 p
= 9 x 14
= 126

Answer(s): 126