Pamela and Gillian have some beads. If Pamela gives 28 beads to Gillian, Gillian will have 5 times the number of beads as Pamela. If Gillian gives 52 beads to Pamela, Pamela will have
35 as many beads as Gillian. How many beads does Pamela have at first?
| |
Case 1 |
Case 2 |
| |
Pamela |
Gillian |
Pamela |
Gillian |
| Before |
4 u + 28 |
20 u - 28 |
9 u - 52 |
15 u + 52 |
| Change |
- 28 |
+ 28 |
+ 52 |
- 52 |
| 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 Pamela had at first is the same in both cases.
9 u - 52 = 4 u + 28
9 u - 4 u = 28 + 52
5 u = 80
1 u = 16
Number of beads that Pamela had at first
= 4 u + 28
= 4 x 16 + 28
= 64 + 28
= 92
Answer(s): 92
