Rachel had four boxes, K, L, M and N which contained a total of 255 mangoes. She transferred 18 mangoes from Box K to Box L, 38 mangoes from Box L to Box M and 75 mangoes from Box M to Box N. The ratio of the number of mangoes in Box K to Box L to Box M changed from  4 : 6 : 11 to 1 : 5 : 9. How many mangoes were in Box N at first?

	Make p the same (1)x5 = (3)	K (1)	L (2)	M	N
Before	20 u	4 u	6 u	11 u	?
Change 1	- 90	- 18	+ 18
Change 2			- 38	+ 38
Change 3				- 75	+ 75
After	5 p	1 p	5 p	9 p	?

4 u - 18 = 1 p --- (1)

6 u + 18 - 38 = 5 p
6 u - 20 = 5 p --- (2)

(1) _{x 5}
20 u - 90 = 5 p --- (3)

Make p the same.

(3) = (2)
20 u - 90 = 6 u - 20
20 u - 6 u = 90 - 20
14 u = 70

1 u = 70 ÷ 14 = 5

Total number of mangoes in Box K, Box L and Box M
= 4 u + 6 u + 11 u
= 21 u

Total number of mangoes in Box N at first
= 255 - 21 u
= 255 - 21 x 5
= 255 - 105
= 150

Answer(s): 150