Gwen and Cathy have some stickers. If Gwen gives 38 stickers to Cathy, Cathy will have 4 times the number of stickers as Gwen. If Cathy gives 18 stickers to Gwen, Gwen will have
35 as many stickers as Cathy. How many stickers does Gwen have at first?
|
Case 1 |
Case 2 |
|
Gwen |
Cathy |
Gwen |
Cathy |
Before |
8 u + 38 |
32 u - 38 |
15 u - 18 |
25 u + 18 |
Change |
- 38 |
+ 38 |
+ 18 |
- 18 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 u |
The total number of stickers in both cases remains unchanged. Make the total number of stickers in both cases the same. LCM of 5 and 8 is 40.
Number of stickers that Gwen had at first is the same in both cases.
15 u - 18 = 8 u + 38
15 u - 8 u = 38 + 18
7 u = 56
1 u = 8
Number of stickers that Gwen had at first
= 8 u + 38
= 8 x 8 + 38
= 64 + 38
= 102
Answer(s): 102