Gabby and Xylia have some beads. If Gabby gives 36 beads to Xylia, Xylia will have 5 times the number of beads as Gabby. If Xylia gives 19 beads to Gabby, Gabby will have
35 as many beads as Xylia. How many beads does Gabby have at first?
|
Case 1 |
Case 2 |
|
Gabby |
Xylia |
Gabby |
Xylia |
Before |
4 u + 36 |
20 u - 36 |
9 u - 19 |
15 u + 19 |
Change |
- 36 |
+ 36 |
+ 19 |
- 19 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 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 8 is 24.
Number of beads that Gabby had at first is the same in both cases.
9 u - 19 = 4 u + 36
9 u - 4 u = 36 + 19
5 u = 55
1 u = 11
Number of beads that Gabby had at first
= 4 u + 36
= 4 x 11 + 36
= 44 + 36
= 80
Answer(s): 80