Eva and Erika have some beads. If Eva gives 26 beads to Erika, Erika will have 4 times the number of beads as Eva. If Erika gives 4 beads to Eva, Eva will have
12 as many beads as Erika. How many beads does Eva have at first?
|
Case 1 |
Case 2 |
|
Eva |
Erika |
Eva |
Erika |
Before |
3 u + 26 |
12 u - 26 |
5 u - 4 |
10 u + 4 |
Change |
- 26 |
+ 26 |
+ 4 |
- 4 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 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 3 is 15.
Number of beads that Eva had at first is the same in both cases.
5 u - 4 = 3 u + 26
5 u - 3 u = 26 + 4
2 u = 30
1 u = 15
Number of beads that Eva had at first
= 3 u + 26
= 3 x 15 + 26
= 45 + 26
= 71
Answer(s): 71