Wendy and Sarah have some marbles. If Wendy gives 11 marbles to Sarah, Sarah will have 5 times the number of marbles as Wendy. If Sarah gives 59 marbles to Wendy, Wendy will have
25 as many marbles as Sarah. How many marbles does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Sarah |
Wendy |
Sarah |
Before |
7 u + 11 |
35 u - 11 |
12 u - 59 |
30 u + 59 |
Change |
- 11 |
+ 11 |
+ 59 |
- 59 |
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 - 59 = 7 u + 11
12 u - 7 u = 11 + 59
5 u = 70
1 u = 14
Number of marbles that Wendy had at first
= 7 u + 11
= 7 x 14 + 11
= 98 + 11
= 109
Answer(s): 109