Cindy and Tiffany have some buttons. If Cindy gives 31 buttons to Tiffany, Tiffany will have 5 times the number of buttons as Cindy. If Tiffany gives 69 buttons to Cindy, Cindy will have
25 as many buttons as Tiffany. How many buttons does Cindy have at first?
|
Case 1 |
Case 2 |
|
Cindy |
Tiffany |
Cindy |
Tiffany |
Before |
7 u + 31 |
35 u - 31 |
12 u - 69 |
30 u + 69 |
Change |
- 31 |
+ 31 |
+ 69 |
- 69 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of buttons that Cindy had at first is the same in both cases.
12 u - 69 = 7 u + 31
12 u - 7 u = 31 + 69
5 u = 100
1 u = 20
Number of buttons that Cindy had at first
= 7 u + 31
= 7 x 20 + 31
= 140 + 31
= 171
Answer(s): 171