Lynn had some fruits at her stall. ¹₃ of them were grapefruits, ¹₄ of the remainder were peaches and the rest were pears. The amounts earned for each grapefruit, each peach and each pear sold are $1.10, $1.30 and $1.40 respectively. The number of grapefruits sold to the number of peaches sold to the number of pears sold was 3 : 2 : 1. In total, she sold ¹₂ of the fruits and earned $43.80. How many grapefruits did she have at first?

Grapefruits	Peaches	Pears	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of peaches and pears is repeated.  Make the total number of peaches and pears the same. LCM of 2 and 4 is 4.

	Grapefruits	Peaches	Pears
Number	3 u	2 u	1 u
Value	$1.10	$1.30	$1.40
Total value	3.3 u	2.6 u	1.4 u

Total amount that Lynn earned
= 3.3 u + 2.6 u + 1.4 u
= 7.3 u

7.3 u = 43.80
 
1 u = 43.80 ÷ 7.3 = 6

Total number of fruits sold
= 3 u + 2 u + 1 u
= 6 u
= 6 x 6
= 36

Total number of fruits at first
= 36 ÷ ¹₂
= 36 x 2
= 72

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

6 p = 72

1 p = 72 ÷ 6 = 12

Number of grapefruits that Lynn had at first
= 2 p
= 2 x 12
= 24

Answer(s): 24