Fanny had some fruits at her stall. ¹₃ of them were mandarin oranges, ³₄ of the remainder were dates and the rest were grapefruits. The amounts earned for each mandarin orange, each date and each grapefruit sold are $1.80, $1.40 and $1.10 respectively. The number of mandarin oranges sold to the number of dates sold to the number of grapefruits sold was 3 : 4 : 1. In total, she sold ¹₃ of the fruits and earned $193.60. How many mandarin oranges did she have at first?

Mandarin Oranges	Dates	Grapefruits	Total
1x2	2x2		3x2
	3x1	1x1
2 p	3 p	1 p	6 p

The total number of dates and grapefruits is repeated.  Make the total number of dates and grapefruits the same. LCM of 2 and 4 is 4.

	Mandarin Oranges	Dates	Grapefruits
Number	3 u	4 u	1 u
Value	$1.80	$1.40	$1.10
Total value	5.4 u	5.6 u	1.1 u

Total amount that Fanny earned
= 5.4 u + 5.6 u + 1.1 u
= 12.1 u

12.1 u = 193.60
 
1 u = 193.60 ÷ 12.1 = 16

Total number of fruits sold
= 3 u + 4 u + 1 u
= 8 u
= 8 x 16
= 128

Total number of fruits at first
= 128 ÷ ¹₃
= 128 x 3
= 384

Total number of fruits at first
= 2 p + 3 p + 1 p
= 6 p

6 p = 384

1 p = 384 ÷ 6 = 64

Number of mandarin oranges that Fanny had at first
= 2 p
= 2 x 64
= 128

Answer(s): 128