Abi had some fruits at her stall. ³₈ of them were coconuts, ¹₂ of the remainder were grapefruits and the rest were mangosteens. The amounts earned for each coconut, each grapefruit and each mangosteen sold are $1.90, $1.60 and $1.70 respectively. The number of coconuts sold to the number of grapefruits sold to the number of mangosteens sold was 3 : 1 : 4. In total, she sold ¹₈ of the fruits and earned $239.70. How many mangosteens did she have at first?

Coconuts	Grapefruits	Mangosteens	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

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

	Coconuts	Grapefruits	Mangosteens
Number	3 u	1 u	4 u
Value	$1.90	$1.60	$1.70
Total value	5.7 u	1.6 u	6.8 u

Total amount that Abi earned
= 5.7 u + 1.6 u + 6.8 u
= 14.1 u

14.1 u = 239.70
 
1 u = 239.70 ÷ 14.1 = 17

Total number of fruits sold
= 3 u + 1 u + 4 u
= 8 u
= 8 x 17
= 136

Total number of fruits at first
= 136 ÷ ¹₈
= 136 x 8
= 1088

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 1088

1 p = 1088 ÷ 16 = 68

Number of mangosteens that Abi had at first
= 5 p
= 5 x 68
= 340

Answer(s): 340