There are some grey and red marbles in a box. If 5 grey marbles are removed from the box, the total number of marbles left will be 8 times the number of grey marbles left. If 33 red marbles are removed from the box, the total number of marbles left will be 4 times the number of grey marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Grey marbles |
Red marbles |
Grey marbles |
Red marbles |
Before |
1 u + 5 |
7 u |
1 p |
3 p + 33 |
Change |
- 5 |
|
|
- 33 |
After |
1 u |
7 u |
1 p |
3 p |
Number of red marbles in the end for Case 1
= 8 u - 1 u
= 7 u
Number of grey marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of grey 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 + 5 = 1 p --- (1)
7 u = 3 p + 33
7 u - 33 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 15 =
3 p --- (3)
(2) = (3)
7 u - 33 = 3 u + 15
7 u - 3 u = 15 + 33
4 u = 48
1 u = 48 ÷ 4 = 12
Number of marbles in the box
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 12) + 5
= 96 + 5
= 101
Answer(s): 101