Shiyun had some fruits at her stall. ³₈ of them were grapefruits, ¹₂ of the remainder were tomatoes and the rest were dragon fruits. The amounts earned for each grapefruit, each tomato and each dragon fruit sold are $1.70, $1.50 and $1.40 respectively. The number of grapefruits sold to the number of tomatoes sold to the number of dragon fruits sold was 5 : 1 : 2. In total, she sold ¹₄ of the fruits and earned $243.20. How many grapefruits did she have at first?

Grapefruits	Tomatoes	Dragon Fruits	Total
3x2	5x2		8x2
	1x5	1x5
6 p	5 p	5 p	16 p

The total number of tomatoes and dragon fruits is repeated.  Make the total number of tomatoes and dragon fruits the same. LCM of 5 and 2 is 10.

	Grapefruits	Tomatoes	Dragon Fruits
Number	5 u	1 u	2 u
Value	$1.70	$1.50	$1.40
Total value	8.5 u	1.5 u	2.8 u

Total amount that Shiyun earned
= 8.5 u + 1.5 u + 2.8 u
= 12.8 u

12.8 u = 243.20
 
1 u = 243.20 ÷ 12.8 = 19

Total number of fruits sold
= 5 u + 1 u + 2 u
= 8 u
= 8 x 19
= 152

Total number of fruits at first
= 152 ÷ ¹₄
= 152 x 4
= 608

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

16 p = 608

1 p = 608 ÷ 16 = 38

Number of grapefruits that Shiyun had at first
= 6 p
= 6 x 38
= 228

Answer(s): 228