There are some brown and pink balls in a container. If 3 brown balls are removed from the container, the total number of balls left will be 8 times the number of brown balls left. If 31 pink balls are removed from the container, the total number of balls left will be 4 times the number of brown balls. How many balls are there in the container?
|
Case 1 |
Case 2 |
|
Brown balls |
Pink balls |
Brown balls |
Pink balls |
Before |
1 u + 3 |
7 u |
1 p |
3 p + 31 |
Change |
- 3 |
|
|
- 31 |
After |
1 u |
7 u |
1 p |
3 p |
Number of pink balls in the end for Case 1
= 8 u - 1 u
= 7 u
Number of brown balls in the end for Case 2
= 4 p - 1 p
= 3 p
The number of brown balls at first is the same for Case 1 and Case 2.
The number of pink balls at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
7 u = 3 p + 31
7 u - 31 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 9 =
3 p --- (3)
(2) = (3)
7 u - 31 = 3 u + 9
7 u - 3 u = 9 + 31
4 u = 40
1 u = 40 ÷ 4 = 10
Number of balls in the container
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 10) + 3
= 80 + 3
= 83
Answer(s): 83