Wendy and Risa have some marbles. If Wendy gives 37 marbles to Risa, Risa will have 5 times the number of marbles as Wendy. If Risa gives 40 marbles to Wendy, Wendy will have
23 as many marbles as Risa. How many marbles does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Risa |
Wendy |
Risa |
Before |
5 u + 37 |
25 u - 37 |
12 u - 40 |
18 u + 40 |
Change |
- 37 |
+ 37 |
+ 40 |
- 40 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of marbles that Wendy had at first is the same in both cases.
12 u - 40 = 5 u + 37
12 u - 5 u = 37 + 40
7 u = 77
1 u = 11
Number of marbles that Wendy had at first
= 5 u + 37
= 5 x 11 + 37
= 55 + 37
= 92
Answer(s): 92