There are some red and grey balls in a container. If 3 red balls are removed from the container, the total number of balls left will be 9 times the number of red balls left. If 18 grey balls are removed from the container, the total number of balls left will be 6 times the number of red balls. How many balls are there in the container?
|
Case 1 |
Case 2 |
|
Red balls |
Grey balls |
Red balls |
Grey balls |
Before |
1 u + 3 |
8 u |
1 p |
5 p + 18 |
Change |
- 3 |
|
|
- 18 |
After |
1 u |
8 u |
1 p |
5 p |
Number of grey balls in the end for Case 1
= 9 u - 1 u
= 8 u
Number of red balls in the end for Case 2
= 6 p - 1 p
= 5 p
The number of red balls at first is the same for Case 1 and Case 2.
The number of grey balls at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
8 u = 5 p + 18
8 u - 18 =
5 p --- (2)
Make p the same.
(1)
x5 5 u + 15 =
5 p --- (3)
(2) = (3)
8 u - 18 = 5 u + 15
8 u - 5 u = 15 + 18
3 u = 33
1 u = 33 ÷ 3 = 11
Number of balls in the container
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 11) + 3
= 99 + 3
= 102
Answer(s): 102