Joelle and Jean have some beads. If Joelle gives 23 beads to Jean, Jean will have 5 times the number of beads as Joelle. If Jean gives 57 beads to Joelle, Joelle will have
35 as many beads as Jean. How many beads does Joelle have at first?
| |
Case 1 |
Case 2 |
| |
Joelle |
Jean |
Joelle |
Jean |
| Before |
4 u + 23 |
20 u - 23 |
9 u - 57 |
15 u + 57 |
| Change |
- 23 |
+ 23 |
+ 57 |
- 57 |
| 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 Joelle had at first is the same in both cases.
9 u - 57 = 4 u + 23
9 u - 4 u = 23 + 57
5 u = 80
1 u = 16
Number of beads that Joelle had at first
= 4 u + 23
= 4 x 16 + 23
= 64 + 23
= 87
Answer(s): 87
