Betty and Gem have some stamps. If Betty gives 37 stamps to Gem, Gem will have 4 times the number of stamps as Betty. If Gem gives 19 stamps to Betty, Betty will have
35 as many stamps as Gem. How many stamps does Betty have at first?
| |
Case 1 |
Case 2 |
| |
Betty |
Gem |
Betty |
Gem |
| Before |
8 u + 37 |
32 u - 37 |
15 u - 19 |
25 u + 19 |
| Change |
- 37 |
+ 37 |
+ 19 |
- 19 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of stamps in both cases remains unchanged. Make the total number of stamps in both cases the same. LCM of 5 and 8 is 40.
Number of stamps that Betty had at first is the same in both cases.
15 u - 19 = 8 u + 37
15 u - 8 u = 37 + 19
7 u = 56
1 u = 8
Number of stamps that Betty had at first
= 8 u + 37
= 8 x 8 + 37
= 64 + 37
= 101
Answer(s): 101
