Gem and Rachel have some stamps. If Gem gives 10 stamps to Rachel, Rachel will have 4 times the number of stamps as Gem. If Rachel gives 8 stamps to Gem, Gem will have
12 as many stamps as Rachel. How many stamps does Gem have at first?
| |
Case 1 |
Case 2 |
| |
Gem |
Rachel |
Gem |
Rachel |
| Before |
3 u + 10 |
12 u - 10 |
5 u - 8 |
10 u + 8 |
| Change |
- 10 |
+ 10 |
+ 8 |
- 8 |
| After |
1x3 =
3 u |
4x3 =
12 u |
1x5 =
5 u |
2x5 =
10 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 3 is 15.
Number of stamps that Gem had at first is the same in both cases.
5 u - 8 = 3 u + 10
5 u - 3 u = 10 + 8
2 u = 18
1 u = 9
Number of stamps that Gem had at first
= 3 u + 10
= 3 x 9 + 10
= 27 + 10
= 37
Answer(s): 37
