Anna had some fruits at her stall. ³₈ of them were apples, ¹₃ of the remainder were dates and the rest were mandarin oranges. The amounts earned for each apple, each date and each mandarin orange sold are $1.80, $1.30 and $1.50 respectively. The number of apples sold to the number of dates sold to the number of mandarin oranges sold was 3 : 5 : 5. In total, she sold ¹₁₂ of the fruits and earned $349.20. How many mandarin oranges did she have at first?

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

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

	Apples	Dates	Mandarin Oranges
Number	3 u	5 u	5 u
Value	$1.80	$1.30	$1.50
Total value	5.4 u	6.5 u	7.5 u

Total amount that Anna earned
= 5.4 u + 6.5 u + 7.5 u
= 19.4 u

19.4 u = 349.20
 
1 u = 349.20 ÷ 19.4 = 18

Total number of fruits sold
= 3 u + 5 u + 5 u
= 13 u
= 13 x 18
= 234

Total number of fruits at first
= 234 ÷ ¹₁₂
= 234 x 12
= 2808

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

24 p = 2808

1 p = 2808 ÷ 24 = 117

Number of mandarin oranges that Anna had at first
= 10 p
= 10 x 117
= 1170

Answer(s): 1170