Tammy and Erika have some beads. If Tammy gives 28 beads to Erika, Erika will have 5 times the number of beads as Tammy. If Erika gives 57 beads to Tammy, Tammy will have
25 as many beads as Erika. How many beads does Tammy have at first?
|
Case 1 |
Case 2 |
|
Tammy |
Erika |
Tammy |
Erika |
Before |
7 u + 28 |
35 u - 28 |
12 u - 57 |
30 u + 57 |
Change |
- 28 |
+ 28 |
+ 57 |
- 57 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of beads that Tammy had at first is the same in both cases.
12 u - 57 = 7 u + 28
12 u - 7 u = 28 + 57
5 u = 85
1 u = 17
Number of beads that Tammy had at first
= 7 u + 28
= 7 x 17 + 28
= 119 + 28
= 147
Answer(s): 147