There are some red and grey beads in a box. If 2 red beads are removed from the box, the total number of beads left will be 6 times the number of red beads left. If 3 grey beads are removed from the box, the total number of beads left will be 5 times the number of red beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Red beads |
Grey beads |
Red beads |
Grey beads |
Before |
1 u + 2 |
5 u |
1 p |
4 p + 3 |
Change |
- 2 |
|
|
- 3 |
After |
1 u |
5 u |
1 p |
4 p |
Number of grey beads in the end for Case 1
= 6 u - 1 u
= 5 u
Number of red beads in the end for Case 2
= 5 p - 1 p
= 4 p
The number of red 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 + 2 = 1 p --- (1)
5 u = 4 p + 3
5 u - 3 =
4 p --- (2)
Make p the same.
(1)
x4 4 u + 8 =
4 p --- (3)
(2) = (3)
5 u - 3 = 4 u + 8
5 u - 4 u = 8 + 3
1 u = 11
1 u = 11 ÷ 1 = 11
Number of beads in the box
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 11) + 2
= 66 + 2
= 68
Answer(s): 68