Shannon and Betty have some beads. If Shannon gives 35 beads to Betty, Betty will have 4 times the number of beads as Shannon. If Betty gives 42 beads to Shannon, Shannon will have
35 as many beads as Betty. How many beads does Shannon have at first?
| |
Case 1 |
Case 2 |
| |
Shannon |
Betty |
Shannon |
Betty |
| Before |
8 u + 35 |
32 u - 35 |
15 u - 42 |
25 u + 42 |
| Change |
- 35 |
+ 35 |
+ 42 |
- 42 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 5 and 8 is 40.
Number of beads that Shannon had at first is the same in both cases.
15 u - 42 = 8 u + 35
15 u - 8 u = 35 + 42
7 u = 77
1 u = 11
Number of beads that Shannon had at first
= 8 u + 35
= 8 x 11 + 35
= 88 + 35
= 123
Answer(s): 123
