Irene and Eva have some buttons. If Irene gives 15 buttons to Eva, Eva will have 4 times the number of buttons as Irene. If Eva gives 13 buttons to Irene, Irene will have
12 as many buttons as Eva. How many buttons does Irene have at first?
| |
Case 1 |
Case 2 |
| |
Irene |
Eva |
Irene |
Eva |
| Before |
3 u + 15 |
12 u - 15 |
5 u - 13 |
10 u + 13 |
| Change |
- 15 |
+ 15 |
+ 13 |
- 13 |
| 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 Irene had at first is the same in both cases.
5 u - 13 = 3 u + 15
5 u - 3 u = 15 + 13
2 u = 28
1 u = 14
Number of buttons that Irene had at first
= 3 u + 15
= 3 x 14 + 15
= 42 + 15
= 57
Answer(s): 57
