Sarah and Xuan have some stickers. If Sarah gives 18 stickers to Xuan, Xuan will have 4 times the number of stickers as Sarah. If Xuan gives 22 stickers to Sarah, Sarah will have
12 as many stickers as Xuan. How many stickers does Sarah have at first?
|
Case 1 |
Case 2 |
|
Sarah |
Xuan |
Sarah |
Xuan |
Before |
3 u + 18 |
12 u - 18 |
5 u - 22 |
10 u + 22 |
Change |
- 18 |
+ 18 |
+ 22 |
- 22 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 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 3 is 15.
Number of stickers that Sarah had at first is the same in both cases.
5 u - 22 = 3 u + 18
5 u - 3 u = 18 + 22
2 u = 40
1 u = 20
Number of stickers that Sarah had at first
= 3 u + 18
= 3 x 20 + 18
= 60 + 18
= 78
Answer(s): 78