There are some grey and yellow beads in a container. If 9 grey beads are removed from the container, the total number of beads left will be 7 times the number of grey beads left. If 9 yellow beads are removed from the container, the total number of beads left will be 4 times the number of grey beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Grey beads |
Yellow beads |
Grey beads |
Yellow beads |
Before |
1 u + 9 |
6 u |
1 p |
3 p + 9 |
Change |
- 9 |
|
|
- 9 |
After |
1 u |
6 u |
1 p |
3 p |
Number of yellow beads in the end for Case 1
= 7 u - 1 u
= 6 u
Number of grey beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of grey beads at first is the same for Case 1 and Case 2.
The number of yellow beads at first is also the same for Case 1 and Case 2.
1 u + 9 = 1 p --- (1)
6 u = 3 p + 9
6 u - 9 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 27 =
3 p --- (3)
(2) = (3)
6 u - 9 = 3 u + 27
6 u - 3 u = 27 + 9
3 u = 36
1 u = 36 ÷ 3 = 12
Number of beads in the container
= (1 u + 9) + 6 u
= 7 u + 9
= (7 x 12) + 9
= 84 + 9
= 93
Answer(s): 93