Rachel had some fruits at her stall. ³₈ of them were grapefruits, ¹₂ of the remainder were guavas and the rest were tomatoes. The amounts earned for each grapefruit, each guava and each tomato sold are $1.20, $1.90 and $1.40 respectively. The number of grapefruits sold to the number of guavas sold to the number of tomatoes sold was 3 : 4 : 1. In total, she sold ¹₄ of the fruits and earned $100.80. How many grapefruits did she have at first?

Grapefruits	Guavas	Tomatoes	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of guavas and tomatoes is repeated.  Make the total number of guavas and tomatoes the same. LCM of 5 and 2 is 10.

	Grapefruits	Guavas	Tomatoes
Number	3 u	4 u	1 u
Value	$1.20	$1.90	$1.40
Total value	3.6 u	7.6 u	1.4 u

Total amount that Rachel earned
= 3.6 u + 7.6 u + 1.4 u
= 12.6 u

12.6 u = 100.80
 
1 u = 100.80 ÷ 12.6 = 8

Total number of fruits sold
= 3 u + 4 u + 1 u
= 8 u
= 8 x 8
= 64

Total number of fruits at first
= 64 ÷ ¹₄
= 64 x 4
= 256

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

16 p = 256

1 p = 256 ÷ 16 = 16

Number of grapefruits that Rachel had at first
= 6 p
= 6 x 16
= 96

Answer(s): 96