There are some purple and red balls in a box. If 3 purple balls are removed from the box, the total number of balls left will be 8 times the number of purple balls left. If 18 red balls are removed from the box, the total number of balls left will be 5 times the number of purple balls. How many balls are there in the box?

	Case 1		Case 2
	Purple balls	Red balls	Purple balls	Red balls
Before	1 u + 3	7 u	1 p	4 p + 18
Change	- 3			- 18
After	1 u	7 u	1 p	4 p

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

Number of purple balls in the end for Case 2
= 5 p - 1 p
= 4 p

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

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

7 u = 4 p + 18
7 u - 18 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 12 = 4 p --- (3)

(2) = (3)
7 u - 18 = 4 u + 12
7 u - 4 u = 12 + 18
3 u = 30

1 u = 30 ÷ 3 = 10

Number of balls in the box
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 10) + 3
= 80 + 3
= 83

Answer(s): 83