Kylie and Jane have some buttons. If Kylie gives 14 buttons to Jane, Jane will have 5 times the number of buttons as Kylie. If Jane gives 16 buttons to Kylie, Kylie will have
35 as many buttons as Jane. How many buttons does Kylie have at first?
|
Case 1 |
Case 2 |
|
Kylie |
Jane |
Kylie |
Jane |
Before |
4 u + 14 |
20 u - 14 |
9 u - 16 |
15 u + 16 |
Change |
- 14 |
+ 14 |
+ 16 |
- 16 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 6 and 8 is 24.
Number of buttons that Kylie had at first is the same in both cases.
9 u - 16 = 4 u + 14
9 u - 4 u = 14 + 16
5 u = 30
1 u = 6
Number of buttons that Kylie had at first
= 4 u + 14
= 4 x 6 + 14
= 24 + 14
= 38
Answer(s): 38