There are some red and pink marbles in a box. If 10 red marbles are removed from the box, the total number of marbles left will be 8 times the number of red marbles left. If 5 pink marbles are removed from the box, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the box?

	Case 1		Case 2
	Red marbles	Pink marbles	Red marbles	Pink marbles
Before	1 u + 10	7 u	1 p	2 p + 5
Change	- 10			- 5
After	1 u	7 u	1 p	2 p

Number of pink marbles in the end for Case 1
= 8 u - 1 u
= 7 u

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

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

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

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

Make p the same.

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

(2) = (3)
7 u - 5 = 2 u + 20
7 u - 2 u = 20 + 5
5 u = 25

1 u = 25 ÷ 5 = 5

Number of marbles in the box
= (1 u + 10) + 7 u
= 8 u + 10
= (8 x 5) + 10
= 40 + 10
= 50

Answer(s): 50