Victoria and Gwen have some stickers. If Victoria gives 38 stickers to Gwen, Gwen will have 5 times the number of stickers as Victoria. If Gwen gives 81 stickers to Victoria, Victoria will have
23 as many stickers as Gwen. How many stickers does Victoria have at first?
|
Case 1 |
Case 2 |
|
Victoria |
Gwen |
Victoria |
Gwen |
Before |
5 u + 38 |
25 u - 38 |
12 u - 81 |
18 u + 81 |
Change |
- 38 |
+ 38 |
+ 81 |
- 81 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of stickers in both cases remains unchanged. Make the total number of stickers in both cases the same. LCM of 6 and 5 is 30.
Number of stickers that Victoria had at first is the same in both cases.
12 u - 81 = 5 u + 38
12 u - 5 u = 38 + 81
7 u = 119
1 u = 17
Number of stickers that Victoria had at first
= 5 u + 38
= 5 x 17 + 38
= 85 + 38
= 123
Answer(s): 123