Joelle and Dana have some beads. If Joelle gives 11 beads to Dana, Dana will have 4 times the number of beads as Joelle. If Dana gives 13 beads to Joelle, Joelle will have
25 as many beads as Dana. How many beads does Joelle have at first?
|
Case 1 |
Case 2 |
|
Joelle |
Dana |
Joelle |
Dana |
Before |
7 u + 11 |
28 u - 11 |
10 u - 13 |
25 u + 13 |
Change |
- 11 |
+ 11 |
+ 13 |
- 13 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 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 7 is 35.
Number of beads that Joelle had at first is the same in both cases.
10 u - 13 = 7 u + 11
10 u - 7 u = 11 + 13
3 u = 24
1 u = 8
Number of beads that Joelle had at first
= 7 u + 11
= 7 x 8 + 11
= 56 + 11
= 67
Answer(s): 67