Sabrina had some fruits at her stall. ³₈ of them were limes, ¹₄ of the remainder were dates and the rest were pears. The amounts earned for each lime, each date and each pear sold are $1.20, $1.70 and $1.40 respectively. The number of limes sold to the number of dates sold to the number of pears sold was 3 : 1 : 4. In total, she sold ¹₈ of the fruits and earned $152.60. How many limes did she have at first?

Limes	Dates	Pears	Total
3x4	5x4		8x4
	1x5	3x5
12 p	5 p	15 p	32 p

The total number of dates and pears is repeated.  Make the total number of dates and pears the same. LCM of 5 and 4 is 20.

	Limes	Dates	Pears
Number	3 u	1 u	4 u
Value	$1.20	$1.70	$1.40
Total value	3.6 u	1.7 u	5.6 u

Total amount that Sabrina earned
= 3.6 u + 1.7 u + 5.6 u
= 10.9 u

10.9 u = 152.60
 
1 u = 152.60 ÷ 10.9 = 14

Total number of fruits sold
= 3 u + 1 u + 4 u
= 8 u
= 8 x 14
= 112

Total number of fruits at first
= 112 ÷ ¹₈
= 112 x 8
= 896

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

32 p = 896

1 p = 896 ÷ 32 = 28

Number of limes that Sabrina had at first
= 12 p
= 12 x 28
= 336

Answer(s): 336