Hilda had some fruits at her stall. ³₈ of them were pomegranates, ¹₂ of the remainder were dragon fruits and the rest were grapefruits. The amounts earned for each pomegranate, each dragon fruit and each grapefruit sold are $1.90, $1.10 and $1.40 respectively. The number of pomegranates sold to the number of dragon fruits sold to the number of grapefruits sold was 1 : 1 : 1. In total, she sold ¹₈ of the fruits and earned $8.80. How many grapefruits did she have at first?

Pomegranates	Dragon Fruits	Grapefruits	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of dragon fruits and grapefruits is repeated.  Make the total number of dragon fruits and grapefruits the same. LCM of 5 and 2 is 10.

	Pomegranates	Dragon Fruits	Grapefruits
Number	1 u	1 u	1 u
Value	$1.90	$1.10	$1.40
Total value	1.9 u	1.1 u	1.4 u

Total amount that Hilda earned
= 1.9 u + 1.1 u + 1.4 u
= 4.4 u

4.4 u = 8.80
 
1 u = 8.80 ÷ 4.4 = 2

Total number of fruits sold
= 1 u + 1 u + 1 u
= 3 u
= 3 x 2
= 6

Total number of fruits at first
= 6 ÷ ¹₈
= 6 x 8
= 48

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 48

1 p = 48 ÷ 16 = 3

Number of grapefruits that Hilda had at first
= 5 p
= 5 x 3
= 15

Answer(s): 15