There are some purple and blue beads in a box. If 5 purple beads are removed from the box, the total number of beads left will be 8 times the number of purple beads left. If 9 blue beads are removed from the box, the total number of beads left will be 4 times the number of purple beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Purple beads |
Blue beads |
Purple beads |
Blue beads |
Before |
1 u + 5 |
7 u |
1 p |
3 p + 9 |
Change |
- 5 |
|
|
- 9 |
After |
1 u |
7 u |
1 p |
3 p |
Number of blue beads in the end for Case 1
= 8 u - 1 u
= 7 u
Number of purple beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of purple beads at first is the same for Case 1 and Case 2.
The number of blue beads at first is also the same for Case 1 and Case 2.
1 u + 5 = 1 p --- (1)
7 u = 3 p + 9
7 u - 9 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 15 =
3 p --- (3)
(2) = (3)
7 u - 9 = 3 u + 15
7 u - 3 u = 15 + 9
4 u = 24
1 u = 24 ÷ 4 = 6
Number of beads in the box
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 6) + 5
= 48 + 5
= 53
Answer(s): 53