Winnie and Roshel have some marbles. If Winnie gives 16 marbles to Roshel, Roshel will have 5 times the number of marbles as Winnie. If Roshel gives 74 marbles to Winnie, Winnie will have
35 as many marbles as Roshel. How many marbles does Winnie have at first?
|
Case 1 |
Case 2 |
|
Winnie |
Roshel |
Winnie |
Roshel |
Before |
4 u + 16 |
20 u - 16 |
9 u - 74 |
15 u + 74 |
Change |
- 16 |
+ 16 |
+ 74 |
- 74 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 6 and 8 is 24.
Number of marbles that Winnie had at first is the same in both cases.
9 u - 74 = 4 u + 16
9 u - 4 u = 16 + 74
5 u = 90
1 u = 18
Number of marbles that Winnie had at first
= 4 u + 16
= 4 x 18 + 16
= 72 + 16
= 88
Answer(s): 88