There are some red and pink beads in a box. If 3 red beads are removed from the box, the total number of beads left will be 9 times the number of red beads left. If 12 pink beads are removed from the box, the total number of beads left will be 3 times the number of red beads. How many beads are there in the box?
|
Case 1 |
Case 2 |
|
Red beads |
Pink beads |
Red beads |
Pink beads |
Before |
1 u + 3 |
8 u |
1 p |
2 p + 12 |
Change |
- 3 |
|
|
- 12 |
After |
1 u |
8 u |
1 p |
2 p |
Number of pink beads in the end for Case 1
= 9 u - 1 u
= 8 u
Number of red beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of red 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 + 3 = 1 p --- (1)
8 u = 2 p + 12
8 u - 12 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 6 =
2 p --- (3)
(2) = (3)
8 u - 12 = 2 u + 6
8 u - 2 u = 6 + 12
6 u = 18
1 u = 18 ÷ 6 = 3
Number of beads in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 3) + 3
= 27 + 3
= 30
Answer(s): 30