There are some pink and grey marbles in a container. If 4 pink marbles are removed from the container, the total number of marbles left will be 9 times the number of pink marbles left. If 7 grey marbles are removed from the container, the total number of marbles left will be 6 times the number of pink marbles. How many marbles are there in the container?

	Case 1		Case 2
	Pink marbles	Grey marbles	Pink marbles	Grey marbles
Before	1 u + 4	8 u	1 p	5 p + 7
Change	- 4			- 7
After	1 u	8 u	1 p	5 p

Number of grey marbles in the end for Case 1
= 9 u - 1 u
= 8 u

Number of pink marbles in the end for Case 2
= 6 p - 1 p
= 5 p

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

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

8 u = 5 p + 7
8 u - 7 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 20 = 5 p --- (3)

(2) = (3)
8 u - 7 = 5 u + 20
8 u - 5 u = 20 + 7
3 u = 27

1 u = 27 ÷ 3 = 9

Number of marbles in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 9) + 4
= 81 + 4
= 85

Answer(s): 85