Olivia had some fruits at her stall. ³₈ of them were peaches, ¹₃ of the remainder were grapefruits and the rest were mandarin oranges. The amounts earned for each peach, each grapefruit and each mandarin orange sold are $1.30, $1.20 and $1.90 respectively. The number of peaches sold to the number of grapefruits sold to the number of mandarin oranges sold was 2 : 3 : 1. In total, she sold ¹₈ of the fruits and earned $137.70. How many mandarin oranges did she have at first?

Peaches	Grapefruits	Mandarin Oranges	Total
3x3	5x3		8x3
	1x5	2x5
9 p	5 p	10 p	24 p

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

	Peaches	Grapefruits	Mandarin Oranges
Number	2 u	3 u	1 u
Value	$1.30	$1.20	$1.90
Total value	2.6 u	3.6 u	1.9 u

Total amount that Olivia earned
= 2.6 u + 3.6 u + 1.9 u
= 8.1 u

8.1 u = 137.70
 
1 u = 137.70 ÷ 8.1 = 17

Total number of fruits sold
= 2 u + 3 u + 1 u
= 6 u
= 6 x 17
= 102

Total number of fruits at first
= 102 ÷ ¹₈
= 102 x 8
= 816

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

24 p = 816

1 p = 816 ÷ 24 = 34

Number of mandarin oranges that Olivia had at first
= 10 p
= 10 x 34
= 340

Answer(s): 340