Gillian and Rachel have some buttons. If Gillian gives 26 buttons to Rachel, Rachel will have 4 times the number of buttons as Gillian. If Rachel gives 4 buttons to Gillian, Gillian will have
25 as many buttons as Rachel. How many buttons does Gillian have at first?
|
Case 1 |
Case 2 |
|
Gillian |
Rachel |
Gillian |
Rachel |
Before |
7 u + 26 |
28 u - 26 |
10 u - 4 |
25 u + 4 |
Change |
- 26 |
+ 26 |
+ 4 |
- 4 |
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 Gillian had at first is the same in both cases.
10 u - 4 = 7 u + 26
10 u - 7 u = 26 + 4
3 u = 30
1 u = 10
Number of buttons that Gillian had at first
= 7 u + 26
= 7 x 10 + 26
= 70 + 26
= 96
Answer(s): 96