Xandra had some fruits at her stall. ³₈ of them were guavas, ¹₂ of the remainder were kiwis and the rest were lemons. The amounts earned for each guava, each kiwi and each lemon sold are $1.10, $1.60 and $1.40 respectively. The number of guavas sold to the number of kiwis sold to the number of lemons sold was 4 : 3 : 4. In total, she sold ¹₈ of the fruits and earned $29.60. How many guavas did she have at first?

Guavas	Kiwis	Lemons	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of kiwis and lemons is repeated.  Make the total number of kiwis and lemons the same. LCM of 5 and 2 is 10.

	Guavas	Kiwis	Lemons
Number	4 u	3 u	4 u
Value	$1.10	$1.60	$1.40
Total value	4.4 u	4.8 u	5.6 u

Total amount that Xandra earned
= 4.4 u + 4.8 u + 5.6 u
= 14.8 u

14.8 u = 29.60
 
1 u = 29.60 ÷ 14.8 = 2

Total number of fruits sold
= 4 u + 3 u + 4 u
= 11 u
= 11 x 2
= 22

Total number of fruits at first
= 22 ÷ ¹₈
= 22 x 8
= 176

Total number of fruits at first
= 6 p + 5 p + 5 p
= 16 p

16 p = 176

1 p = 176 ÷ 16 = 11

Number of guavas that Xandra had at first
= 6 p
= 6 x 11
= 66

Answer(s): 66