Gem and Wendy have some buttons. If Gem gives 17 buttons to Wendy, Wendy will have 4 times the number of buttons as Gem. If Wendy gives 116 buttons to Gem, Gem will have
35 as many buttons as Wendy. How many buttons does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Wendy |
Gem |
Wendy |
Before |
8 u + 17 |
32 u - 17 |
15 u - 116 |
25 u + 116 |
Change |
- 17 |
+ 17 |
+ 116 |
- 116 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 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 8 is 40.
Number of buttons that Gem had at first is the same in both cases.
15 u - 116 = 8 u + 17
15 u - 8 u = 17 + 116
7 u = 133
1 u = 19
Number of buttons that Gem had at first
= 8 u + 17
= 8 x 19 + 17
= 152 + 17
= 169
Answer(s): 169