There are some blue and pink beads in a box. If 4 blue beads are removed from the box, the total number of beads left will be 8 times the number of blue beads left. If 37 pink beads are removed from the box, the total number of beads left will be 3 times the number of blue beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Blue beads |
Pink beads |
Blue beads |
Pink beads |
Before |
1 u + 4 |
7 u |
1 p |
2 p + 37 |
Change |
- 4 |
|
|
- 37 |
After |
1 u |
7 u |
1 p |
2 p |
Number of pink beads in the end for Case 1
= 8 u - 1 u
= 7 u
Number of blue beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of blue beads at first is the same for Case 1 and Case 2.
The number of pink beads at first is also the same for Case 1 and Case 2.
1 u + 4 = 1 p --- (1)
7 u = 2 p + 37
7 u - 37 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 8 =
2 p --- (3)
(2) = (3)
7 u - 37 = 2 u + 8
7 u - 2 u = 8 + 37
5 u = 45
1 u = 45 ÷ 5 = 9
Number of beads in the box
= (1 u + 4) + 7 u
= 8 u + 4
= (8 x 9) + 4
= 72 + 4
= 76
Answer(s): 76