Tammy had some fruits at her stall. ¹₃ of them were mandarin oranges, ¹₄ of the remainder were pomegranates and the rest were tomatoes. The amounts earned for each mandarin orange, each pomegranate and each tomato sold are $1.30, $1.80 and $1.60 respectively. The number of mandarin oranges sold to the number of pomegranates sold to the number of tomatoes sold was 2 : 3 : 4. In total, she sold ¹₂ of the fruits and earned $259.20. How many mandarin oranges did she have at first?

Mandarin Oranges	Pomegranates	Tomatoes	Total
1x2	2x2		3x2
	1x1	3x1
2 p	1 p	3 p	6 p

The total number of pomegranates and tomatoes is repeated.  Make the total number of pomegranates and tomatoes the same. LCM of 2 and 4 is 4.

	Mandarin Oranges	Pomegranates	Tomatoes
Number	2 u	3 u	4 u
Value	$1.30	$1.80	$1.60
Total value	2.6 u	5.4 u	6.4 u

Total amount that Tammy earned
= 2.6 u + 5.4 u + 6.4 u
= 14.4 u

14.4 u = 259.20
 
1 u = 259.20 ÷ 14.4 = 18

Total number of fruits sold
= 2 u + 3 u + 4 u
= 9 u
= 9 x 18
= 162

Total number of fruits at first
= 162 ÷ ¹₂
= 162 x 2
= 324

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

6 p = 324

1 p = 324 ÷ 6 = 54

Number of mandarin oranges that Tammy had at first
= 2 p
= 2 x 54
= 108

Answer(s): 108