Yen had some fruits at her stall. ¹₃ of them were avocados, ¹₅ of the remainder were mandarin oranges and the rest were pears. The amounts earned for each avocado, each mandarin orange and each pear sold are $1.50, $1.80 and $1.60 respectively. The number of avocados sold to the number of mandarin oranges sold to the number of pears sold was 1 : 2 : 2. In total, she sold ¹₅ of the fruits and earned $74.70. How many avocados did she have at first?

Avocados	Mandarin Oranges	Pears	Total
1x5	2x5		3x5
	1x2	4x2
5 p	2 p	8 p	15 p

The total number of mandarin oranges and pears is repeated.  Make the total number of mandarin oranges and pears the same. LCM of 2 and 5 is 10.

	Avocados	Mandarin Oranges	Pears
Number	1 u	2 u	2 u
Value	$1.50	$1.80	$1.60
Total value	1.5 u	3.6 u	3.2 u

Total amount that Yen earned
= 1.5 u + 3.6 u + 3.2 u
= 8.3 u

8.3 u = 74.70
 
1 u = 74.70 ÷ 8.3 = 9

Total number of fruits sold
= 1 u + 2 u + 2 u
= 5 u
= 5 x 9
= 45

Total number of fruits at first
= 45 ÷ ¹₅
= 45 x 5
= 225

Total number of fruits at first
= 5 p + 2 p + 8 p
= 15 p

15 p = 225

1 p = 225 ÷ 15 = 15

Number of avocados that Yen had at first
= 5 p
= 5 x 15
= 75

Answer(s): 75