Xuan and Erika have some beads. If Xuan gives 27 beads to Erika, Erika will have 3 times the number of beads as Xuan. If Erika gives 30 beads to Xuan, Xuan will have
23 as many beads as Erika. How many beads does Xuan have at first?
| |
Case 1 |
Case 2 |
| |
Xuan |
Erika |
Xuan |
Erika |
| Before |
5 u + 27 |
15 u - 27 |
8 u - 30 |
12 u + 30 |
| Change |
- 27 |
+ 27 |
+ 30 |
- 30 |
| 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 Xuan had at first is the same in both cases.
8 u - 30 = 5 u + 27
8 u - 5 u = 27 + 30
3 u = 57
1 u = 19
Number of beads that Xuan had at first
= 5 u + 27
= 5 x 19 + 27
= 95 + 27
= 122
Answer(s): 122
