Kylie and Olivia have some beads. If Kylie gives 32 beads to Olivia, Olivia will have 5 times the number of beads as Kylie. If Olivia gives 3 beads to Kylie, Kylie will have
25 as many beads as Olivia. How many beads does Kylie have at first?
|
Case 1 |
Case 2 |
|
Kylie |
Olivia |
Kylie |
Olivia |
Before |
7 u + 32 |
35 u - 32 |
12 u - 3 |
30 u + 3 |
Change |
- 32 |
+ 32 |
+ 3 |
- 3 |
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 Kylie had at first is the same in both cases.
12 u - 3 = 7 u + 32
12 u - 7 u = 32 + 3
5 u = 35
1 u = 7
Number of beads that Kylie had at first
= 7 u + 32
= 7 x 7 + 32
= 49 + 32
= 81
Answer(s): 81