Lynn had some fruits at her stall. ³₈ of them were oranges, ¹₄ of the remainder were mandarin oranges and the rest were grapefruits. The amounts earned for each orange, each mandarin orange and each grapefruit sold are $1.40, $1.30 and $1.10 respectively. The number of oranges sold to the number of mandarin oranges sold to the number of grapefruits sold was 4 : 1 : 5. In total, she sold ¹₈ of the fruits and earned $173.60. How many oranges did she have at first?

Oranges	Mandarin Oranges	Grapefruits	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

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

	Oranges	Mandarin Oranges	Grapefruits
Number	4 u	1 u	5 u
Value	$1.40	$1.30	$1.10
Total value	5.6 u	1.3 u	5.5 u

Total amount that Lynn earned
= 5.6 u + 1.3 u + 5.5 u
= 12.4 u

12.4 u = 173.60
 
1 u = 173.60 ÷ 12.4 = 14

Total number of fruits sold
= 4 u + 1 u + 5 u
= 10 u
= 10 x 14
= 140

Total number of fruits at first
= 140 ÷ ¹₈
= 140 x 8
= 1120

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

32 p = 1120

1 p = 1120 ÷ 32 = 35

Number of oranges that Lynn had at first
= 12 p
= 12 x 35
= 420

Answer(s): 420