There are some purple and grey beads in a box. If 2 purple beads are removed from the box, the total number of beads left will be 9 times the number of purple beads left. If 24 grey beads are removed from the box, the total number of beads left will be 5 times the number of purple beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Purple beads |
Grey beads |
Purple beads |
Grey beads |
Before |
1 u + 2 |
8 u |
1 p |
4 p + 24 |
Change |
- 2 |
|
|
- 24 |
After |
1 u |
8 u |
1 p |
4 p |
Number of grey beads in the end for Case 1
= 9 u - 1 u
= 8 u
Number of purple beads in the end for Case 2
= 5 p - 1 p
= 4 p
The number of purple 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)
8 u = 4 p + 24
8 u - 24 =
4 p --- (2)
Make p the same.
(1)
x4 4 u + 8 =
4 p --- (3)
(2) = (3)
8 u - 24 = 4 u + 8
8 u - 4 u = 8 + 24
4 u = 32
1 u = 32 ÷ 4 = 8
Number of beads in the box
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 8) + 2
= 72 + 2
= 74
Answer(s): 74