There are some gold and yellow balls in a box. If 7 gold balls are removed from the box, the total number of balls left will be 7 times the number of gold balls left. If 26 yellow balls are removed from the box, the total number of balls left will be 3 times the number of gold balls. How many balls are there in the box?

	Case 1		Case 2
	Gold balls	Yellow balls	Gold balls	Yellow balls
Before	1 u + 7	6 u	1 p	2 p + 26
Change	- 7			- 26
After	1 u	6 u	1 p	2 p

Number of yellow balls in the end for Case 1
= 7 u - 1 u
= 6 u

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

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

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

6 u = 2 p + 26
6 u - 26 = 2 p --- (2)

Make p the same.

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

(2) = (3)
6 u - 26 = 2 u + 14
6 u - 2 u = 14 + 26
4 u = 40

1 u = 40 ÷ 4 = 10

Number of balls in the box
= (1 u + 7) + 6 u
= 7 u + 7
= (7 x 10) + 7
= 70 + 7
= 77

Answer(s): 77