Usha had some fruits at her stall. ³₈ of them were mandarin oranges, ¹₃ of the remainder were avocados and the rest were dates. The amounts earned for each mandarin orange, each avocado and each date sold are $1.80, $1.90 and $1.70 respectively. The number of mandarin oranges sold to the number of avocados sold to the number of dates sold was 3 : 5 : 1. In total, she sold ¹₄ of the fruits and earned $298.80. How many dates did she have at first?

Mandarin Oranges	Avocados	Dates	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

The total number of avocados and dates is repeated.  Make the total number of avocados and dates the same. LCM of 5 and 3 is 15.

	Mandarin Oranges	Avocados	Dates
Number	3 u	5 u	1 u
Value	$1.80	$1.90	$1.70
Total value	5.4 u	9.5 u	1.7 u

Total amount that Usha earned
= 5.4 u + 9.5 u + 1.7 u
= 16.6 u

16.6 u = 298.80
 
1 u = 298.80 ÷ 16.6 = 18

Total number of fruits sold
= 3 u + 5 u + 1 u
= 9 u
= 9 x 18
= 162

Total number of fruits at first
= 162 ÷ ¹₄
= 162 x 4
= 648

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

24 p = 648

1 p = 648 ÷ 24 = 27

Number of dates that Usha had at first
= 10 p
= 10 x 27
= 270

Answer(s): 270