There are some purple and yellow balls in a container. If 10 purple balls are removed from the container, the total number of balls left will be 8 times the number of purple balls left. If 10 yellow balls are removed from the container, the total number of balls left will be 4 times the number of purple balls. How many balls are there in the container?
|
Case 1 |
Case 2 |
|
Purple balls |
Yellow balls |
Purple balls |
Yellow balls |
Before |
1 u + 10 |
7 u |
1 p |
3 p + 10 |
Change |
- 10 |
|
|
- 10 |
After |
1 u |
7 u |
1 p |
3 p |
Number of yellow balls in the end for Case 1
= 8 u - 1 u
= 7 u
Number of purple balls in the end for Case 2
= 4 p - 1 p
= 3 p
The number of purple balls at first is the same for Case 1 and Case 2.
The number of yellow balls at first is also the same for Case 1 and Case 2.
1 u + 10 = 1 p --- (1)
7 u = 3 p + 10
7 u - 10 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 30 =
3 p --- (3)
(2) = (3)
7 u - 10 = 3 u + 30
7 u - 3 u = 30 + 10
4 u = 40
1 u = 40 ÷ 4 = 10
Number of balls in the container
= (1 u + 10) + 7 u
= 8 u + 10
= (8 x 10) + 10
= 80 + 10
= 90
Answer(s): 90