Tiffany and Risa have some buttons. If Tiffany gives 37 buttons to Risa, Risa will have 5 times the number of buttons as Tiffany. If Risa gives 3 buttons to Tiffany, Tiffany will have
25 as many buttons as Risa. How many buttons does Tiffany have at first?
| |
Case 1 |
Case 2 |
| |
Tiffany |
Risa |
Tiffany |
Risa |
| Before |
7 u + 37 |
35 u - 37 |
12 u - 3 |
30 u + 3 |
| Change |
- 37 |
+ 37 |
+ 3 |
- 3 |
| 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 Tiffany had at first is the same in both cases.
12 u - 3 = 7 u + 37
12 u - 7 u = 37 + 3
5 u = 40
1 u = 8
Number of buttons that Tiffany had at first
= 7 u + 37
= 7 x 8 + 37
= 56 + 37
= 93
Answer(s): 93
