There are some green and red beads in a box. If 8 green beads are removed from the box, the total number of beads left will be 9 times the number of green beads left. If 12 red beads are removed from the box, the total number of beads left will be 5 times the number of green beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Green beads |
Red beads |
Green beads |
Red beads |
Before |
1 u + 8 |
8 u |
1 p |
4 p + 12 |
Change |
- 8 |
|
|
- 12 |
After |
1 u |
8 u |
1 p |
4 p |
Number of red beads in the end for Case 1
= 9 u - 1 u
= 8 u
Number of green beads in the end for Case 2
= 5 p - 1 p
= 4 p
The number of green beads at first is the same for Case 1 and Case 2.
The number of red beads at first is also the same for Case 1 and Case 2.
1 u + 8 = 1 p --- (1)
8 u = 4 p + 12
8 u - 12 =
4 p --- (2)
Make p the same.
(1)
x4 4 u + 32 =
4 p --- (3)
(2) = (3)
8 u - 12 = 4 u + 32
8 u - 4 u = 32 + 12
4 u = 44
1 u = 44 ÷ 4 = 11
Number of beads in the box
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 11) + 8
= 99 + 8
= 107
Answer(s): 107