There are some purple and brown marbles in a container. If 10 purple marbles are removed from the container, the total number of marbles left will be 9 times the number of purple marbles left. If 34 brown marbles are removed from the container, the total number of marbles left will be 3 times the number of purple marbles. How many marbles are there in the container?

	Case 1		Case 2
	Purple marbles	Brown marbles	Purple marbles	Brown marbles
Before	1 u + 10	8 u	1 p	2 p + 34
Change	- 10			- 34
After	1 u	8 u	1 p	2 p

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

Number of purple marbles in the end for Case 2
= 3 p - 1 p
= 2 p

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

1 u + 10 = 1 p --- (1)

8 u = 2 p + 34
8 u - 34 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 20 = 2 p --- (3)

(2) = (3)
8 u - 34 = 2 u + 20
8 u - 2 u = 20 + 34
6 u = 54

1 u = 54 ÷ 6 = 9

Number of marbles in the container
= (1 u + 10) + 8 u
= 9 u + 10
= (9 x 9) + 10
= 81 + 10
= 91

Answer(s): 91