Min and Erika have some buttons. If Min gives 40 buttons to Erika, Erika will have 5 times the number of buttons as Min. If Erika gives 9 buttons to Min, Min will have
23 as many buttons as Erika. How many buttons does Min have at first?
|
Case 1 |
Case 2 |
|
Min |
Erika |
Min |
Erika |
Before |
5 u + 40 |
25 u - 40 |
12 u - 9 |
18 u + 9 |
Change |
- 40 |
+ 40 |
+ 9 |
- 9 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of buttons that Min had at first is the same in both cases.
12 u - 9 = 5 u + 40
12 u - 5 u = 40 + 9
7 u = 49
1 u = 7
Number of buttons that Min had at first
= 5 u + 40
= 5 x 7 + 40
= 35 + 40
= 75
Answer(s): 75