There are some blue and black balls in a box. If 7 blue balls are removed from the box, the total number of balls left will be 9 times the number of blue balls left. If 34 black balls are removed from the box, the total number of balls left will be 3 times the number of blue balls. How many balls are there in the box?

	Case 1		Case 2
	Blue balls	Black balls	Blue balls	Black balls
Before	1 u + 7	8 u	1 p	2 p + 34
Change	- 7			- 34
After	1 u	8 u	1 p	2 p

Number of black balls in the end for Case 1
= 9 u - 1 u
= 8 u

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

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

1 u + 7 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 14 = 2 p --- (3)

(2) = (3)
8 u - 34 = 2 u + 14
8 u - 2 u = 14 + 34
6 u = 48

1 u = 48 ÷ 6 = 8

Number of balls in the box
= (1 u + 7) + 8 u
= 9 u + 7
= (9 x 8) + 7
= 72 + 7
= 79

Answer(s): 79