Joelle and Fanny have some beads. If Joelle gives 18 beads to Fanny, Fanny will have 5 times the number of beads as Joelle. If Fanny gives 47 beads to Joelle, Joelle will have
25 as many beads as Fanny. How many beads does Joelle have at first?
|
Case 1 |
Case 2 |
|
Joelle |
Fanny |
Joelle |
Fanny |
Before |
7 u + 18 |
35 u - 18 |
12 u - 47 |
30 u + 47 |
Change |
- 18 |
+ 18 |
+ 47 |
- 47 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of beads that Joelle had at first is the same in both cases.
12 u - 47 = 7 u + 18
12 u - 7 u = 18 + 47
5 u = 65
1 u = 13
Number of beads that Joelle had at first
= 7 u + 18
= 7 x 13 + 18
= 91 + 18
= 109
Answer(s): 109