There are some black and green beads in a box. If 2 black beads are removed from the box, the total number of beads left will be 5 times the number of black beads left. If 2 green beads are removed from the box, the total number of beads left will be 3 times the number of black beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Black beads |
Green beads |
Black beads |
Green beads |
Before |
1 u + 2 |
4 u |
1 p |
2 p + 2 |
Change |
- 2 |
|
|
- 2 |
After |
1 u |
4 u |
1 p |
2 p |
Number of green beads in the end for Case 1
= 5 u - 1 u
= 4 u
Number of black beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of black beads at first is the same for Case 1 and Case 2.
The number of green beads at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
4 u = 2 p + 2
4 u - 2 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 4 =
2 p --- (3)
(2) = (3)
4 u - 2 = 2 u + 4
4 u - 2 u = 4 + 2
2 u = 6
1 u = 6 ÷ 2 = 3
Number of beads in the box
= (1 u + 2) + 4 u
= 5 u + 2
= (5 x 3) + 2
= 15 + 2
= 17
Answer(s): 17