Tammy had some fruits at her stall. ³₈ of them were mangosteens, ²₃ of the remainder were peaches and the rest were oranges. The amounts earned for each mangosteen, each peach and each orange sold are $1.60, $1.50 and $1.40 respectively. The number of mangosteens sold to the number of peaches sold to the number of oranges sold was 2 : 3 : 3. In total, she sold ¹₁₂ of the fruits and earned $202.30. How many mangosteens did she have at first?

Mangosteens	Peaches	Oranges	Total
3x3	5x3		8x3
	2x5	1x5
9 p	10 p	5 p	24 p

The total number of peaches and oranges is repeated.  Make the total number of peaches and oranges the same. LCM of 5 and 3 is 15.

	Mangosteens	Peaches	Oranges
Number	2 u	3 u	3 u
Value	$1.60	$1.50	$1.40
Total value	3.2 u	4.5 u	4.2 u

Total amount that Tammy earned
= 3.2 u + 4.5 u + 4.2 u
= 11.9 u

11.9 u = 202.30
 
1 u = 202.30 ÷ 11.9 = 17

Total number of fruits sold
= 2 u + 3 u + 3 u
= 8 u
= 8 x 17
= 136

Total number of fruits at first
= 136 ÷ ¹₁₂
= 136 x 12
= 1632

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

24 p = 1632

1 p = 1632 ÷ 24 = 68

Number of mangosteens that Tammy had at first
= 9 p
= 9 x 68
= 612

Answer(s): 612