There are some purple and yellow marbles in a container. If 7 purple marbles are removed from the container, the total number of marbles left will be 8 times the number of purple marbles left. If 19 yellow marbles are removed from the container, the total number of marbles left will be 4 times the number of purple marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Purple marbles |
Yellow marbles |
Purple marbles |
Yellow marbles |
Before |
1 u + 7 |
7 u |
1 p |
3 p + 19 |
Change |
- 7 |
|
|
- 19 |
After |
1 u |
7 u |
1 p |
3 p |
Number of yellow marbles in the end for Case 1
= 8 u - 1 u
= 7 u
Number of purple marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of purple marbles at first is the same for Case 1 and Case 2.
The number of yellow marbles at first is also the same for Case 1 and Case 2.
1 u + 7 = 1 p --- (1)
7 u = 3 p + 19
7 u - 19 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 21 =
3 p --- (3)
(2) = (3)
7 u - 19 = 3 u + 21
7 u - 3 u = 21 + 19
4 u = 40
1 u = 40 ÷ 4 = 10
Number of marbles in the container
= (1 u + 7) + 7 u
= 8 u + 7
= (8 x 10) + 7
= 80 + 7
= 87
Answer(s): 87