There are some grey and green balls in a box. If 7 grey balls are removed from the box, the total number of balls left will be 8 times the number of grey balls left. If 11 green balls are removed from the box, the total number of balls left will be 3 times the number of grey balls. How many balls are there in the box?

	Case 1		Case 2
	Grey balls	Green balls	Grey balls	Green balls
Before	1 u + 7	7 u	1 p	2 p + 11
Change	- 7			- 11
After	1 u	7 u	1 p	2 p

Number of green balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of grey balls in the end for Case 2
= 3 p - 1 p
= 2 p

The number of grey balls at first is the same for Case 1 and Case 2.
The number of green balls at first is also the same for Case 1 and Case 2.

1 u + 7 = 1 p --- (1)

7 u = 2 p + 11
7 u - 11 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 14 = 2 p --- (3)

(2) = (3)
7 u - 11 = 2 u + 14
7 u - 2 u = 14 + 11
5 u = 25

1 u = 25 ÷ 5 = 5

Number of balls in the box
= (1 u + 7) + 7 u
= 8 u + 7
= (8 x 5) + 7
= 40 + 7
= 47

Answer(s): 47