Penelope had some fruits at her stall. ³₈ of them were plums, ¹₃ of the remainder were apricots and the rest were oranges. The amounts earned for each plum, each apricot and each orange sold are $1.40, $1.80 and $1.10 respectively. The number of plums sold to the number of apricots sold to the number of oranges sold was 3 : 3 : 2. In total, she sold ¹₁₂ of the fruits and earned $70.80. How many oranges did she have at first?

Plums	Apricots	Oranges	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Plums	Apricots	Oranges
Number	3 u	3 u	2 u
Value	$1.40	$1.80	$1.10
Total value	4.2 u	5.4 u	2.2 u

Total amount that Penelope earned
= 4.2 u + 5.4 u + 2.2 u
= 11.8 u

11.8 u = 70.80
 
1 u = 70.80 ÷ 11.8 = 6

Total number of fruits sold
= 3 u + 3 u + 2 u
= 8 u
= 8 x 6
= 48

Total number of fruits at first
= 48 ÷ ¹₁₂
= 48 x 12
= 576

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

24 p = 576

1 p = 576 ÷ 24 = 24

Number of oranges that Penelope had at first
= 10 p
= 10 x 24
= 240

Answer(s): 240