Tom and Will had some buttons in the ratio of 5 : 3. Will and Archie had some buttons in the ratio of 4 : 3. Tom sold 84 buttons to Archie and ended up with half the number of buttons Will had. How many buttons did Archie have in the end?
| Tom |
Will |
Archie |
| 5x4 |
3x4 |
|
| |
4x3 |
3x3 |
| 20 u |
12 u |
9 u |
The number of buttons that Will had at first is repeated. Make the number of buttons that Will had at first the same. LCM of 3 and 4 is 12.
| |
Tom |
Will |
Archie |
| Before |
20 u |
12 u |
9 u |
| Change |
- 84 |
|
+ 84 |
| After |
6 u |
12 u |
9 u + 84 |
Number of buttons that Tom had in the end
= 12 u ÷ 2
= 6 u
Number of buttons that Tom sold to Archie
= 20 u - 6 u
= 14 u
14 u = 84
1 u = 84 ÷ 14 = 6
Number of buttons that Archie had in the end
= 9 u + 84
= 9 x 6 + 84
= 54 + 84
= 138
Answer(s): 138
