There are some purple and gold balls in a box. If 2 purple balls are removed from the box, the total number of balls left will be 7 times the number of purple balls left. If 9 gold balls are removed from the box, the total number of balls left will be 4 times the number of purple balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
Purple balls |
Gold balls |
Purple balls |
Gold balls |
Before |
1 u + 2 |
6 u |
1 p |
3 p + 9 |
Change |
- 2 |
|
|
- 9 |
After |
1 u |
6 u |
1 p |
3 p |
Number of gold balls in the end for Case 1
= 7 u - 1 u
= 6 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 gold balls at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
6 u = 3 p + 9
6 u - 9 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 6 =
3 p --- (3)
(2) = (3)
6 u - 9 = 3 u + 6
6 u - 3 u = 6 + 9
3 u = 15
1 u = 15 ÷ 3 = 5
Number of balls in the box
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 5) + 2
= 35 + 2
= 37
Answer(s): 37