There are some black and grey beads in a box. If 5 black beads are removed from the box, the total number of beads left will be 9 times the number of black beads left. If 44 grey 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 |
Grey beads |
Black beads |
Grey beads |
Before |
1 u + 5 |
8 u |
1 p |
2 p + 44 |
Change |
- 5 |
|
|
- 44 |
After |
1 u |
8 u |
1 p |
2 p |
Number of grey beads in the end for Case 1
= 9 u - 1 u
= 8 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 grey beads at first is also the same for Case 1 and Case 2.
1 u + 5 = 1 p --- (1)
8 u = 2 p + 44
8 u - 44 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 10 =
2 p --- (3)
(2) = (3)
8 u - 44 = 2 u + 10
8 u - 2 u = 10 + 44
6 u = 54
1 u = 54 ÷ 6 = 9
Number of beads in the box
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 9) + 5
= 81 + 5
= 86
Answer(s): 86