There are some green and red marbles in a box. If 4 green marbles are removed from the box, the total number of marbles left will be 9 times the number of green marbles left. If 34 red marbles are removed from the box, the total number of marbles left will be 3 times the number of green marbles. How many marbles are there in the box?

	Case 1		Case 2
	Green marbles	Red marbles	Green marbles	Red marbles
Before	1 u + 4	8 u	1 p	2 p + 34
Change	- 4			- 34
After	1 u	8 u	1 p	2 p

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

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

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

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

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

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
8 u - 34 = 2 u + 8
8 u - 2 u = 8 + 34
6 u = 42

1 u = 42 ÷ 6 = 7

Number of marbles in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 7) + 4
= 63 + 4
= 67

Answer(s): 67