There are some purple and brown balls in a container. If 5 purple balls are removed from the container, the total number of balls left will be 8 times the number of purple balls left. If 25 brown balls are removed from the container, the total number of balls left will be 4 times the number of purple balls. How many balls are there in the container?

	Case 1		Case 2
	Purple balls	Brown balls	Purple balls	Brown balls
Before	1 u + 5	7 u	1 p	3 p + 25
Change	- 5			- 25
After	1 u	7 u	1 p	3 p

Number of brown balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of purple balls in the end for Case 2
= 4 p - 1 p
= 3 p

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

1 u + 5 = 1 p --- (1)

7 u = 3 p + 25
7 u - 25 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 15 = 3 p --- (3)

(2) = (3)
7 u - 25 = 3 u + 15
7 u - 3 u = 15 + 25
4 u = 40

1 u = 40 ÷ 4 = 10

Number of balls in the container
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 10) + 5
= 80 + 5
= 85

Answer(s): 85