Abi and Julie have some buttons. If Abi gives 26 buttons to Julie, Julie will have 4 times the number of buttons as Abi. If Julie gives 107 buttons to Abi, Abi will have
35 as many buttons as Julie. How many buttons does Abi have at first?
|
Case 1 |
Case 2 |
|
Abi |
Julie |
Abi |
Julie |
Before |
8 u + 26 |
32 u - 26 |
15 u - 107 |
25 u + 107 |
Change |
- 26 |
+ 26 |
+ 107 |
- 107 |
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 Abi had at first is the same in both cases.
15 u - 107 = 8 u + 26
15 u - 8 u = 26 + 107
7 u = 133
1 u = 19
Number of buttons that Abi had at first
= 8 u + 26
= 8 x 19 + 26
= 152 + 26
= 178
Answer(s): 178