Jaslyn had some fruits at her stall. ³₈ of them were grapefruits, ¹₃ of the remainder were lemons and the rest were dragon fruits. The amounts earned for each grapefruit, each lemon and each dragon fruit sold are $1.40, $1.10 and $1.70 respectively. The number of grapefruits sold to the number of lemons sold to the number of dragon fruits sold was 3 : 4 : 3. In total, she sold ¹₆ of the fruits and earned $82.20. How many grapefruits did she have at first?

Grapefruits	Lemons	Dragon Fruits	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of lemons and dragon fruits is repeated.  Make the total number of lemons and dragon fruits the same. LCM of 5 and 3 is 15.

	Grapefruits	Lemons	Dragon Fruits
Number	3 u	4 u	3 u
Value	$1.40	$1.10	$1.70
Total value	4.2 u	4.4 u	5.1 u

Total amount that Jaslyn earned
= 4.2 u + 4.4 u + 5.1 u
= 13.7 u

13.7 u = 82.20
 
1 u = 82.20 ÷ 13.7 = 6

Total number of fruits sold
= 3 u + 4 u + 3 u
= 10 u
= 10 x 6
= 60

Total number of fruits at first
= 60 ÷ ¹₆
= 60 x 6
= 360

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

24 p = 360

1 p = 360 ÷ 24 = 15

Number of grapefruits that Jaslyn had at first
= 9 p
= 9 x 15
= 135

Answer(s): 135