Winnie and Gillian have some buttons. If Winnie gives 30 buttons to Gillian, Gillian will have 5 times the number of buttons as Winnie. If Gillian gives 15 buttons to Winnie, Winnie will have
25 as many buttons as Gillian. How many buttons does Winnie have at first?
|
Case 1 |
Case 2 |
|
Winnie |
Gillian |
Winnie |
Gillian |
Before |
7 u + 30 |
35 u - 30 |
12 u - 15 |
30 u + 15 |
Change |
- 30 |
+ 30 |
+ 15 |
- 15 |
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 Winnie had at first is the same in both cases.
12 u - 15 = 7 u + 30
12 u - 7 u = 30 + 15
5 u = 45
1 u = 9
Number of buttons that Winnie had at first
= 7 u + 30
= 7 x 9 + 30
= 63 + 30
= 93
Answer(s): 93