Gem and Min have some beads. If Gem gives 24 beads to Min, Min will have 5 times the number of beads as Gem. If Min gives 66 beads to Gem, Gem will have
35 as many beads as Min. How many beads does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Min |
Gem |
Min |
Before |
4 u + 24 |
20 u - 24 |
9 u - 66 |
15 u + 66 |
Change |
- 24 |
+ 24 |
+ 66 |
- 66 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 6 and 8 is 24.
Number of beads that Gem had at first is the same in both cases.
9 u - 66 = 4 u + 24
9 u - 4 u = 24 + 66
5 u = 90
1 u = 18
Number of beads that Gem had at first
= 4 u + 24
= 4 x 18 + 24
= 72 + 24
= 96
Answer(s): 96