Wendy and Winnie have some erasers. If Wendy gives 22 erasers to Winnie, Winnie will have 4 times the number of erasers as Wendy. If Winnie gives 62 erasers to Wendy, Wendy will have
35 as many erasers as Winnie. How many erasers does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Winnie |
Wendy |
Winnie |
Before |
8 u + 22 |
32 u - 22 |
15 u - 62 |
25 u + 62 |
Change |
- 22 |
+ 22 |
+ 62 |
- 62 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 5 and 8 is 40.
Number of erasers that Wendy had at first is the same in both cases.
15 u - 62 = 8 u + 22
15 u - 8 u = 22 + 62
7 u = 84
1 u = 12
Number of erasers that Wendy had at first
= 8 u + 22
= 8 x 12 + 22
= 96 + 22
= 118
Answer(s): 118