Archie and Paul had some pens in the ratio of 5 : 4. Paul and Ethan had some pens in the ratio of 9 : 7. Archie sold 108 pens to Ethan and ended up with half the number of pens Paul had. How many pens did Ethan have in the end?
| Archie |
Paul |
Ethan |
| 5x9 |
4x9 |
|
| |
9x4 |
7x4 |
| 45 u |
36 u |
28 u |
The number of pens that Paul had at first is repeated. Make the number of pens that Paul had at first the same. LCM of 4 and 9 is 36.
| |
Archie |
Paul |
Ethan |
| Before |
45 u |
36 u |
28 u |
| Change |
- 108 |
|
+ 108 |
| After |
18 u |
36 u |
28 u + 108 |
Number of pens that Archie had in the end
= 36 u ÷ 2
= 18 u
Number of pens that Archie sold to Ethan
= 45 u - 18 u
= 27 u
27 u = 108
1 u = 108 ÷ 27 = 4
Number of pens that Ethan had in the end
= 28 u + 108
= 28 x 4 + 108
= 112 + 108
= 220
Answer(s): 220
