Shiyun had some fruits at her stall. ¹₃ of them were mangosteens, ¹₄ of the remainder were dragon fruits and the rest were lemons. The amounts earned for each mangosteen, each dragon fruit and each lemon sold are $1.20, $1.50 and $1.60 respectively. The number of mangosteens sold to the number of dragon fruits sold to the number of lemons sold was 4 : 5 : 3. In total, she sold ¹₃ of the fruits and earned $256.50. How many mangosteens did she have at first?

Mangosteens	Dragon Fruits	Lemons	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

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

	Mangosteens	Dragon Fruits	Lemons
Number	4 u	5 u	3 u
Value	$1.20	$1.50	$1.60
Total value	4.8 u	7.5 u	4.8 u

Total amount that Shiyun earned
= 4.8 u + 7.5 u + 4.8 u
= 17.1 u

17.1 u = 256.50
 
1 u = 256.50 ÷ 17.1 = 15

Total number of fruits sold
= 4 u + 5 u + 3 u
= 12 u
= 12 x 15
= 180

Total number of fruits at first
= 180 ÷ ¹₃
= 180 x 3
= 540

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

6 p = 540

1 p = 540 ÷ 6 = 90

Number of mangosteens that Shiyun had at first
= 2 p
= 2 x 90
= 180

Answer(s): 180