Emily had some fruits at her stall. ¹₃ of them were pomegranates, ³₄ of the remainder were kiwis and the rest were grapefruits. The amounts earned for each pomegranate, each kiwi and each grapefruit sold are $1.80, $1.20 and $1.60 respectively. The number of pomegranates sold to the number of kiwis sold to the number of grapefruits sold was 1 : 3 : 4. In total, she sold ¹₃ of the fruits and earned $153.40. How many pomegranates did she have at first?

Pomegranates	Kiwis	Grapefruits	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of kiwis and grapefruits is repeated.  Make the total number of kiwis and grapefruits the same. LCM of 2 and 4 is 4.

	Pomegranates	Kiwis	Grapefruits
Number	1 u	3 u	4 u
Value	$1.80	$1.20	$1.60
Total value	1.8 u	3.6 u	6.4 u

Total amount that Emily earned
= 1.8 u + 3.6 u + 6.4 u
= 11.8 u

11.8 u = 153.40
 
1 u = 153.40 ÷ 11.8 = 13

Total number of fruits sold
= 1 u + 3 u + 4 u
= 8 u
= 8 x 13
= 104

Total number of fruits at first
= 104 ÷ ¹₃
= 104 x 3
= 312

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

6 p = 312

1 p = 312 ÷ 6 = 52

Number of pomegranates that Emily had at first
= 2 p
= 2 x 52
= 104

Answer(s): 104