Fiona had some fruits at her stall. ¹₃ of them were guavas, ³₄ of the remainder were dragon fruits and the rest were pomegranates. The amounts earned for each guava, each dragon fruit and each pomegranate sold are $1.10, $1.40 and $1.20 respectively. The number of guavas sold to the number of dragon fruits sold to the number of pomegranates sold was 2 : 2 : 3. In total, she sold ¹₂ of the fruits and earned $77.40. How many guavas did she have at first?

Guavas	Dragon Fruits	Pomegranates	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of dragon fruits and pomegranates is repeated.  Make the total number of dragon fruits and pomegranates the same. LCM of 2 and 4 is 4.

	Guavas	Dragon Fruits	Pomegranates
Number	2 u	2 u	3 u
Value	$1.10	$1.40	$1.20
Total value	2.2 u	2.8 u	3.6 u

Total amount that Fiona earned
= 2.2 u + 2.8 u + 3.6 u
= 8.6 u

8.6 u = 77.40
 
1 u = 77.40 ÷ 8.6 = 9

Total number of fruits sold
= 2 u + 2 u + 3 u
= 7 u
= 7 x 9
= 63

Total number of fruits at first
= 63 ÷ ¹₂
= 63 x 2
= 126

Total number of fruits at first
= 2 p + 3 p + 1 p
= 6 p

6 p = 126

1 p = 126 ÷ 6 = 21

Number of guavas that Fiona had at first
= 2 p
= 2 x 21
= 42

Answer(s): 42