Eva and Victoria have some buttons. If Eva gives 31 buttons to Victoria, Victoria will have 4 times the number of buttons as Eva. If Victoria gives 53 buttons to Eva, Eva will have
35 as many buttons as Victoria. How many buttons does Eva have at first?
| |
Case 1 |
Case 2 |
| |
Eva |
Victoria |
Eva |
Victoria |
| Before |
8 u + 31 |
32 u - 31 |
15 u - 53 |
25 u + 53 |
| Change |
- 31 |
+ 31 |
+ 53 |
- 53 |
| 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 Eva had at first is the same in both cases.
15 u - 53 = 8 u + 31
15 u - 8 u = 31 + 53
7 u = 84
1 u = 12
Number of buttons that Eva had at first
= 8 u + 31
= 8 x 12 + 31
= 96 + 31
= 127
Answer(s): 127
