Rachel had some fruits at her stall. ³₈ of them were grapefruits, ³₄ of the remainder were avocados and the rest were tomatoes. The amounts earned for each grapefruit, each avocado and each tomato sold are $1.20, $1.80 and $1.90 respectively. The number of grapefruits sold to the number of avocados sold to the number of tomatoes sold was 2 : 1 : 5. In total, she sold ¹₈ of the fruits and earned $123.30. How many tomatoes did she have at first?

Grapefruits	Avocados	Tomatoes	Total
3x4	5x4		8x4
	3x5	1x5
12 p	15 p	5 p	32 p

The total number of avocados and tomatoes is repeated.  Make the total number of avocados and tomatoes the same. LCM of 5 and 4 is 20.

	Grapefruits	Avocados	Tomatoes
Number	2 u	1 u	5 u
Value	$1.20	$1.80	$1.90
Total value	2.4 u	1.8 u	9.5 u

Total amount that Rachel earned
= 2.4 u + 1.8 u + 9.5 u
= 13.7 u

13.7 u = 123.30
 
1 u = 123.30 ÷ 13.7 = 9

Total number of fruits sold
= 2 u + 1 u + 5 u
= 8 u
= 8 x 9
= 72

Total number of fruits at first
= 72 ÷ ¹₈
= 72 x 8
= 576

Total number of fruits at first
= 12 p + 15 p + 5 p
= 32 p

32 p = 576

1 p = 576 ÷ 32 = 18

Number of tomatoes that Rachel had at first
= 5 p
= 5 x 18
= 90

Answer(s): 90