There are some white and yellow marbles in a container. If 4 white marbles are removed from the container, the total number of marbles left will be 9 times the number of white marbles left. If 28 yellow marbles are removed from the container, the total number of marbles left will be 3 times the number of white marbles. How many marbles are there in the container?

	Case 1		Case 2
	White marbles	Yellow marbles	White marbles	Yellow marbles
Before	1 u + 4	8 u	1 p	2 p + 28
Change	- 4			- 28
After	1 u	8 u	1 p	2 p

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

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

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

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

8 u = 2 p + 28
8 u - 28 = 2 p --- (2)

Make p the same.

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

(2) = (3)
8 u - 28 = 2 u + 8
8 u - 2 u = 8 + 28
6 u = 36

1 u = 36 ÷ 6 = 6

Number of marbles in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 6) + 4
= 54 + 4
= 58

Answer(s): 58