Nicole had some fruits at her stall. ¹₃ of them were guavas, ¹₅ of the remainder were oranges and the rest were mangosteens. The amounts earned for each guava, each orange and each mangosteen sold are $1.60, $1.40 and $1.30 respectively. The number of guavas sold to the number of oranges sold to the number of mangosteens sold was 2 : 2 : 5. In total, she sold ¹₅ of the fruits and earned $87.50. How many mangosteens did she have at first?

Guavas	Oranges	Mangosteens	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of oranges and mangosteens is repeated.  Make the total number of oranges and mangosteens the same. LCM of 2 and 5 is 10.

	Guavas	Oranges	Mangosteens
Number	2 u	2 u	5 u
Value	$1.60	$1.40	$1.30
Total value	3.2 u	2.8 u	6.5 u

Total amount that Nicole earned
= 3.2 u + 2.8 u + 6.5 u
= 12.5 u

12.5 u = 87.50
 
1 u = 87.50 ÷ 12.5 = 7

Total number of fruits sold
= 2 u + 2 u + 5 u
= 9 u
= 9 x 7
= 63

Total number of fruits at first
= 63 ÷ ¹₅
= 63 x 5
= 315

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 315

1 p = 315 ÷ 15 = 21

Number of mangosteens that Nicole had at first
= 8 p
= 8 x 21
= 168

Answer(s): 168