There are some gold and pink beads in a container. If 7 gold beads are removed from the container, the total number of beads left will be 9 times the number of gold beads left. If 34 pink beads are removed from the container, the total number of beads left will be 4 times the number of gold beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Gold beads |
Pink beads |
Gold beads |
Pink beads |
Before |
1 u + 7 |
8 u |
1 p |
3 p + 34 |
Change |
- 7 |
|
|
- 34 |
After |
1 u |
8 u |
1 p |
3 p |
Number of pink beads in the end for Case 1
= 9 u - 1 u
= 8 u
Number of gold beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of gold 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 + 7 = 1 p --- (1)
8 u = 3 p + 34
8 u - 34 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 21 =
3 p --- (3)
(2) = (3)
8 u - 34 = 3 u + 21
8 u - 3 u = 21 + 34
5 u = 55
1 u = 55 ÷ 5 = 11
Number of beads in the container
= (1 u + 7) + 8 u
= 9 u + 7
= (9 x 11) + 7
= 99 + 7
= 106
Answer(s): 106