Fanny and Ivory have some buttons. If Fanny gives 18 buttons to Ivory, Ivory will have 5 times the number of buttons as Fanny. If Ivory gives 22 buttons to Fanny, Fanny will have
25 as many buttons as Ivory. How many buttons does Fanny have at first?
|
Case 1 |
Case 2 |
|
Fanny |
Ivory |
Fanny |
Ivory |
Before |
7 u + 18 |
35 u - 18 |
12 u - 22 |
30 u + 22 |
Change |
- 18 |
+ 18 |
+ 22 |
- 22 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 6 and 7 is 42.
Number of buttons that Fanny had at first is the same in both cases.
12 u - 22 = 7 u + 18
12 u - 7 u = 18 + 22
5 u = 40
1 u = 8
Number of buttons that Fanny had at first
= 7 u + 18
= 7 x 8 + 18
= 56 + 18
= 74
Answer(s): 74