Betty and Cathy have some stickers. If Betty gives 36 stickers to Cathy, Cathy will have 3 times the number of stickers as Betty. If Cathy gives 24 stickers to Betty, Betty will have
23 as many stickers as Cathy. How many stickers does Betty have at first?
|
Case 1 |
Case 2 |
|
Betty |
Cathy |
Betty |
Cathy |
Before |
5 u + 36 |
15 u - 36 |
8 u - 24 |
12 u + 24 |
Change |
- 36 |
+ 36 |
+ 24 |
- 24 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of stickers in both cases remains unchanged. Make the total number of stickers in both cases the same. LCM of 4 and 5 is 20.
Number of stickers that Betty had at first is the same in both cases.
8 u - 24 = 5 u + 36
8 u - 5 u = 36 + 24
3 u = 60
1 u = 20
Number of stickers that Betty had at first
= 5 u + 36
= 5 x 20 + 36
= 100 + 36
= 136
Answer(s): 136