Diana and Fanny have some buttons. If Diana gives 16 buttons to Fanny, Fanny will have 4 times the number of buttons as Diana. If Fanny gives 44 buttons to Diana, Diana will have
25 as many buttons as Fanny. How many buttons does Diana have at first?
|
Case 1 |
Case 2 |
|
Diana |
Fanny |
Diana |
Fanny |
Before |
7 u + 16 |
28 u - 16 |
10 u - 44 |
25 u + 44 |
Change |
- 16 |
+ 16 |
+ 44 |
- 44 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 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 7 is 35.
Number of buttons that Diana had at first is the same in both cases.
10 u - 44 = 7 u + 16
10 u - 7 u = 16 + 44
3 u = 60
1 u = 20
Number of buttons that Diana had at first
= 7 u + 16
= 7 x 20 + 16
= 140 + 16
= 156
Answer(s): 156