Tammy and Diana have some buttons. If Tammy gives 29 buttons to Diana, Diana will have 5 times the number of buttons as Tammy. If Diana gives 16 buttons to Tammy, Tammy will have
25 as many buttons as Diana. How many buttons does Tammy have at first?
|
Case 1 |
Case 2 |
|
Tammy |
Diana |
Tammy |
Diana |
Before |
7 u + 29 |
35 u - 29 |
12 u - 16 |
30 u + 16 |
Change |
- 29 |
+ 29 |
+ 16 |
- 16 |
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 Tammy had at first is the same in both cases.
12 u - 16 = 7 u + 29
12 u - 7 u = 29 + 16
5 u = 45
1 u = 9
Number of buttons that Tammy had at first
= 7 u + 29
= 7 x 9 + 29
= 63 + 29
= 92
Answer(s): 92