There are some gold and yellow beads in a box. If 7 gold beads are removed from the box, the total number of beads left will be 9 times the number of gold beads left. If 58 yellow beads are removed from the box, the total number of beads left will be 3 times the number of gold beads. How many beads are there in the box?

	Case 1		Case 2
	Gold beads	Yellow beads	Gold beads	Yellow beads
Before	1 u + 7	8 u	1 p	2 p + 58
Change	- 7			- 58
After	1 u	8 u	1 p	2 p

Number of yellow beads in the end for Case 1
= 9 u - 1 u
= 8 u

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

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

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

8 u = 2 p + 58
8 u - 58 = 2 p --- (2)

Make p the same.

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

(2) = (3)
8 u - 58 = 2 u + 14
8 u - 2 u = 14 + 58
6 u = 72

1 u = 72 ÷ 6 = 12

Number of beads in the box
= (1 u + 7) + 8 u
= 9 u + 7
= (9 x 12) + 7
= 108 + 7
= 115

Answer(s): 115