Victoria had some fruits at her stall. ³₈ of them were grapefruits, ²₃ of the remainder were lemons and the rest were coconuts. The amounts earned for each grapefruit, each lemon and each coconut sold are $1.50, $1.20 and $1.70 respectively. The number of grapefruits sold to the number of lemons sold to the number of coconuts sold was 5 : 2 : 1. In total, she sold ¹₈ of the fruits and earned $34.80. How many grapefruits did she have at first?

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

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

	Grapefruits	Lemons	Coconuts
Number	5 u	2 u	1 u
Value	$1.50	$1.20	$1.70
Total value	7.5 u	2.4 u	1.7 u

Total amount that Victoria earned
= 7.5 u + 2.4 u + 1.7 u
= 11.6 u

11.6 u = 34.80
 
1 u = 34.80 ÷ 11.6 = 3

Total number of fruits sold
= 5 u + 2 u + 1 u
= 8 u
= 8 x 3
= 24

Total number of fruits at first
= 24 ÷ ¹₈
= 24 x 8
= 192

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

24 p = 192

1 p = 192 ÷ 24 = 8

Number of grapefruits that Victoria had at first
= 9 p
= 9 x 8
= 72

Answer(s): 72