Pamela and Victoria have some beads. If Pamela gives 21 beads to Victoria, Victoria will have 5 times the number of beads as Pamela. If Victoria gives 35 beads to Pamela, Pamela will have
23 as many beads as Victoria. How many beads does Pamela have at first?
| |
Case 1 |
Case 2 |
| |
Pamela |
Victoria |
Pamela |
Victoria |
| Before |
5 u + 21 |
25 u - 21 |
12 u - 35 |
18 u + 35 |
| Change |
- 21 |
+ 21 |
+ 35 |
- 35 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 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 5 is 30.
Number of beads that Pamela had at first is the same in both cases.
12 u - 35 = 5 u + 21
12 u - 5 u = 21 + 35
7 u = 56
1 u = 8
Number of beads that Pamela had at first
= 5 u + 21
= 5 x 8 + 21
= 40 + 21
= 61
Answer(s): 61
