Lucy had four boxes, K, L, M and N which contained a total of 190 passion fruits. She transferred 20 passion fruits from Box K to Box L, 46 passion fruits from Box L to Box M and 78 passion fruits from Box M to Box N. The ratio of the number of passion fruits in Box K to Box L to Box M changed from  4 : 7 : 10 to 1 : 4 : 7. How many passion fruits were in Box N at first?

	Make p the same (1)x4 = (3)	K (1)	L (2)	M	N
Before	16 u	4 u	7 u	10 u	?
Change 1	- 80	- 20	+ 20
Change 2			- 46	+ 46
Change 3				- 78	+ 78
After	4 p	1 p	4 p	7 p	?

4 u - 20 = 1 p --- (1)

7 u + 20 - 46 = 4 p
7 u - 26 = 4 p --- (2)

(1) _{x 4}
16 u - 80 = 4 p --- (3)

Make p the same.

(3) = (2)
16 u - 80 = 7 u - 26
16 u - 7 u = 80 - 26
9 u = 54

1 u = 54 ÷ 9 = 6

Total number of passion fruits in Box K, Box L and Box M
= 4 u + 7 u + 10 u
= 21 u

Total number of passion fruits in Box N at first
= 190 - 21 u
= 190 - 21 x 6
= 190 - 126
= 64

Answer(s): 64