Tammy and Olivia have some beads. If Tammy gives 20 beads to Olivia, Olivia will have 4 times the number of beads as Tammy. If Olivia gives 19 beads to Tammy, Tammy will have
25 as many beads as Olivia. How many beads does Tammy have at first?
|
Case 1 |
Case 2 |
|
Tammy |
Olivia |
Tammy |
Olivia |
Before |
7 u + 20 |
28 u - 20 |
10 u - 19 |
25 u + 19 |
Change |
- 20 |
+ 20 |
+ 19 |
- 19 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 5 and 7 is 35.
Number of beads that Tammy had at first is the same in both cases.
10 u - 19 = 7 u + 20
10 u - 7 u = 20 + 19
3 u = 39
1 u = 13
Number of beads that Tammy had at first
= 7 u + 20
= 7 x 13 + 20
= 91 + 20
= 111
Answer(s): 111