Erika and Raeann have some buttons. If Erika gives 37 buttons to Raeann, Raeann will have 3 times the number of buttons as Erika. If Raeann gives 5 buttons to Erika, Erika will have
23 as many buttons as Raeann. How many buttons does Erika have at first?
| |
Case 1 |
Case 2 |
| |
Erika |
Raeann |
Erika |
Raeann |
| Before |
5 u + 37 |
15 u - 37 |
8 u - 5 |
12 u + 5 |
| Change |
- 37 |
+ 37 |
+ 5 |
- 5 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 4 and 5 is 20.
Number of buttons that Erika had at first is the same in both cases.
8 u - 5 = 5 u + 37
8 u - 5 u = 37 + 5
3 u = 42
1 u = 14
Number of buttons that Erika had at first
= 5 u + 37
= 5 x 14 + 37
= 70 + 37
= 107
Answer(s): 107
