Cindy had some fruits at her stall. ³₈ of them were pears, ¹₄ of the remainder were oranges and the rest were mandarin oranges. The amounts earned for each pear, each orange and each mandarin orange sold are $1.30, $1.10 and $1.20 respectively. The number of pears sold to the number of oranges sold to the number of mandarin oranges sold was 5 : 2 : 3. In total, she sold ¹₁₆ of the fruits and earned $110.70. How many pears did she have at first?

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

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

	Pears	Oranges	Mandarin Oranges
Number	5 u	2 u	3 u
Value	$1.30	$1.10	$1.20
Total value	6.5 u	2.2 u	3.6 u

Total amount that Cindy earned
= 6.5 u + 2.2 u + 3.6 u
= 12.3 u

12.3 u = 110.70
 
1 u = 110.70 ÷ 12.3 = 9

Total number of fruits sold
= 5 u + 2 u + 3 u
= 10 u
= 10 x 9
= 90

Total number of fruits at first
= 90 ÷ ¹₁₆
= 90 x 16
= 1440

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

32 p = 1440

1 p = 1440 ÷ 32 = 45

Number of pears that Cindy had at first
= 12 p
= 12 x 45
= 540

Answer(s): 540