Lynn and Rachel have some buttons. If Lynn gives 40 buttons to Rachel, Rachel will have 5 times the number of buttons as Lynn. If Rachel gives 51 buttons to Lynn, Lynn will have
23 as many buttons as Rachel. How many buttons does Lynn have at first?
|
Case 1 |
Case 2 |
|
Lynn |
Rachel |
Lynn |
Rachel |
Before |
5 u + 40 |
25 u - 40 |
12 u - 51 |
18 u + 51 |
Change |
- 40 |
+ 40 |
+ 51 |
- 51 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of buttons that Lynn had at first is the same in both cases.
12 u - 51 = 5 u + 40
12 u - 5 u = 40 + 51
7 u = 91
1 u = 13
Number of buttons that Lynn had at first
= 5 u + 40
= 5 x 13 + 40
= 65 + 40
= 105
Answer(s): 105