Gabby and Fiona have some beads. If Gabby gives 32 beads to Fiona, Fiona will have 5 times the number of beads as Gabby. If Fiona gives 28 beads to Gabby, Gabby will have
35 as many beads as Fiona. How many beads does Gabby have at first?
| |
Case 1 |
Case 2 |
| |
Gabby |
Fiona |
Gabby |
Fiona |
| Before |
4 u + 32 |
20 u - 32 |
9 u - 28 |
15 u + 28 |
| Change |
- 32 |
+ 32 |
+ 28 |
- 28 |
| 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 - 28 = 4 u + 32
9 u - 4 u = 32 + 28
5 u = 60
1 u = 12
Number of beads that Gabby had at first
= 4 u + 32
= 4 x 12 + 32
= 48 + 32
= 80
Answer(s): 80
