There are some yellow and red marbles in a box. If 7 yellow marbles are removed from the box, the total number of marbles left will be 9 times the number of yellow marbles left. If 40 red marbles are removed from the box, the total number of marbles left will be 3 times the number of yellow marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Yellow marbles |
Red marbles |
Yellow marbles |
Red marbles |
Before |
1 u + 7 |
8 u |
1 p |
2 p + 40 |
Change |
- 7 |
|
|
- 40 |
After |
1 u |
8 u |
1 p |
2 p |
Number of red marbles in the end for Case 1
= 9 u - 1 u
= 8 u
Number of yellow marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of yellow 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 + 7 = 1 p --- (1)
8 u = 2 p + 40
8 u - 40 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 14 =
2 p --- (3)
(2) = (3)
8 u - 40 = 2 u + 14
8 u - 2 u = 14 + 40
6 u = 54
1 u = 54 ÷ 6 = 9
Number of marbles in the box
= (1 u + 7) + 8 u
= 9 u + 7
= (9 x 9) + 7
= 81 + 7
= 88
Answer(s): 88