Tina and Eva have some beads. If Tina gives 11 beads to Eva, Eva will have 3 times the number of beads as Tina. If Eva gives 25 beads to Tina, Tina will have
23 as many beads as Eva. How many beads does Tina have at first?
| |
Case 1 |
Case 2 |
| |
Tina |
Eva |
Tina |
Eva |
| Before |
5 u + 11 |
15 u - 11 |
8 u - 25 |
12 u + 25 |
| Change |
- 11 |
+ 11 |
+ 25 |
- 25 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 4 and 5 is 20.
Number of beads that Tina had at first is the same in both cases.
8 u - 25 = 5 u + 11
8 u - 5 u = 11 + 25
3 u = 36
1 u = 12
Number of beads that Tina had at first
= 5 u + 11
= 5 x 12 + 11
= 60 + 11
= 71
Answer(s): 71
