Elyse and Xuan have some buttons. If Elyse gives 34 buttons to Xuan, Xuan will have 3 times the number of buttons as Elyse. If Xuan gives 2 buttons to Elyse, Elyse will have
23 as many buttons as Xuan. How many buttons does Elyse have at first?
| |
Case 1 |
Case 2 |
| |
Elyse |
Xuan |
Elyse |
Xuan |
| Before |
5 u + 34 |
15 u - 34 |
8 u - 2 |
12 u + 2 |
| Change |
- 34 |
+ 34 |
+ 2 |
- 2 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 4 and 5 is 20.
Number of buttons that Elyse had at first is the same in both cases.
8 u - 2 = 5 u + 34
8 u - 5 u = 34 + 2
3 u = 36
1 u = 12
Number of buttons that Elyse had at first
= 5 u + 34
= 5 x 12 + 34
= 60 + 34
= 94
Answer(s): 94
