Xandra and Tina have some buttons. If Xandra gives 14 buttons to Tina, Tina will have 4 times the number of buttons as Xandra. If Tina gives 24 buttons to Xandra, Xandra will have
12 as many buttons as Tina. How many buttons does Xandra have at first?
|
Case 1 |
Case 2 |
|
Xandra |
Tina |
Xandra |
Tina |
Before |
3 u + 14 |
12 u - 14 |
5 u - 24 |
10 u + 24 |
Change |
- 14 |
+ 14 |
+ 24 |
- 24 |
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 Xandra had at first is the same in both cases.
5 u - 24 = 3 u + 14
5 u - 3 u = 14 + 24
2 u = 38
1 u = 19
Number of buttons that Xandra had at first
= 3 u + 14
= 3 x 19 + 14
= 57 + 14
= 71
Answer(s): 71