There are some green and red marbles in a box. If 3 green marbles are removed from the box, the total number of marbles left will be 5 times the number of green marbles left. If 12 red marbles are removed from the box, the total number of marbles left will be 3 times the number of green marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Green marbles |
Red marbles |
Green marbles |
Red marbles |
Before |
1 u + 3 |
4 u |
1 p |
2 p + 12 |
Change |
- 3 |
|
|
- 12 |
After |
1 u |
4 u |
1 p |
2 p |
Number of red marbles in the end for Case 1
= 5 u - 1 u
= 4 u
Number of green marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of green marbles at first is the same for Case 1 and Case 2.
The number of red marbles at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
4 u = 2 p + 12
4 u - 12 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 6 =
2 p --- (3)
(2) = (3)
4 u - 12 = 2 u + 6
4 u - 2 u = 6 + 12
2 u = 18
1 u = 18 ÷ 2 = 9
Number of marbles in the box
= (1 u + 3) + 4 u
= 5 u + 3
= (5 x 9) + 3
= 45 + 3
= 48
Answer(s): 48