Emily had some fruits at her stall. ³₈ of them were mandarin oranges, ¹₂ of the remainder were dragon fruits and the rest were pomegranates. The amounts earned for each mandarin orange, each dragon fruit and each pomegranate sold are $1.10, $1.20 and $1.60 respectively. The number of mandarin oranges sold to the number of dragon fruits sold to the number of pomegranates sold was 4 : 1 : 2. In total, she sold ¹₈ of the fruits and earned $158.40. How many mandarin oranges did she have at first?

Mandarin Oranges	Dragon Fruits	Pomegranates	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of dragon fruits and pomegranates is repeated.  Make the total number of dragon fruits and pomegranates the same. LCM of 5 and 2 is 10.

	Mandarin Oranges	Dragon Fruits	Pomegranates
Number	4 u	1 u	2 u
Value	$1.10	$1.20	$1.60
Total value	4.4 u	1.2 u	3.2 u

Total amount that Emily earned
= 4.4 u + 1.2 u + 3.2 u
= 8.8 u

8.8 u = 158.40
 
1 u = 158.40 ÷ 8.8 = 18

Total number of fruits sold
= 4 u + 1 u + 2 u
= 7 u
= 7 x 18
= 126

Total number of fruits at first
= 126 ÷ ¹₈
= 126 x 8
= 1008

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 1008

1 p = 1008 ÷ 16 = 63

Number of mandarin oranges that Emily had at first
= 6 p
= 6 x 63
= 378

Answer(s): 378