Raeann and Fiona have some buttons. If Raeann gives 31 buttons to Fiona, Fiona will have 4 times the number of buttons as Raeann. If Fiona gives 29 buttons to Raeann, Raeann will have
25 as many buttons as Fiona. How many buttons does Raeann have at first?
|
Case 1 |
Case 2 |
|
Raeann |
Fiona |
Raeann |
Fiona |
Before |
7 u + 31 |
28 u - 31 |
10 u - 29 |
25 u + 29 |
Change |
- 31 |
+ 31 |
+ 29 |
- 29 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 5 and 7 is 35.
Number of buttons that Raeann had at first is the same in both cases.
10 u - 29 = 7 u + 31
10 u - 7 u = 31 + 29
3 u = 60
1 u = 20
Number of buttons that Raeann had at first
= 7 u + 31
= 7 x 20 + 31
= 140 + 31
= 171
Answer(s): 171