Wendy and Kimberly have some marbles. If Wendy gives 23 marbles to Kimberly, Kimberly will have 5 times the number of marbles as Wendy. If Kimberly gives 27 marbles to Wendy, Wendy will have
25 as many marbles as Kimberly. How many marbles does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Kimberly |
Wendy |
Kimberly |
Before |
7 u + 23 |
35 u - 23 |
12 u - 27 |
30 u + 27 |
Change |
- 23 |
+ 23 |
+ 27 |
- 27 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of marbles that Wendy had at first is the same in both cases.
12 u - 27 = 7 u + 23
12 u - 7 u = 23 + 27
5 u = 50
1 u = 10
Number of marbles that Wendy had at first
= 7 u + 23
= 7 x 10 + 23
= 70 + 23
= 93
Answer(s): 93