Marion had some fruits at her stall. ³₈ of them were guavas, ¹₄ of the remainder were oranges and the rest were dates. The amounts earned for each guava, each orange and each date sold are $1.80, $1.60 and $1.50 respectively. The number of guavas sold to the number of oranges sold to the number of dates sold was 4 : 4 : 3. In total, she sold ¹₁₆ of the fruits and earned $144.80. How many dates did she have at first?

Guavas	Oranges	Dates	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of oranges and dates is repeated.  Make the total number of oranges and dates the same. LCM of 5 and 4 is 20.

	Guavas	Oranges	Dates
Number	4 u	4 u	3 u
Value	$1.80	$1.60	$1.50
Total value	7.2 u	6.4 u	4.5 u

Total amount that Marion earned
= 7.2 u + 6.4 u + 4.5 u
= 18.1 u

18.1 u = 144.80
 
1 u = 144.80 ÷ 18.1 = 8

Total number of fruits sold
= 4 u + 4 u + 3 u
= 11 u
= 11 x 8
= 88

Total number of fruits at first
= 88 ÷ ¹₁₆
= 88 x 16
= 1408

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

32 p = 1408

1 p = 1408 ÷ 32 = 44

Number of dates that Marion had at first
= 15 p
= 15 x 44
= 660

Answer(s): 660