Erika and Xuan have some buttons. If Erika gives 10 buttons to Xuan, Xuan will have 4 times the number of buttons as Erika. If Xuan gives 4 buttons to Erika, Erika will have
12 as many buttons as Xuan. How many buttons does Erika have at first?
| |
Case 1 |
Case 2 |
| |
Erika |
Xuan |
Erika |
Xuan |
| Before |
3 u + 10 |
12 u - 10 |
5 u - 4 |
10 u + 4 |
| Change |
- 10 |
+ 10 |
+ 4 |
- 4 |
| After |
1x3 =
3 u |
4x3 =
12 u |
1x5 =
5 u |
2x5 =
10 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 3 is 15.
Number of buttons that Erika had at first is the same in both cases.
5 u - 4 = 3 u + 10
5 u - 3 u = 10 + 4
2 u = 14
1 u = 7
Number of buttons that Erika had at first
= 3 u + 10
= 3 x 7 + 10
= 21 + 10
= 31
Answer(s): 31
