Archie, Ken and Howard have some pens. The ratios of their pens are as follows:
Archie : (Archie + Ken + Howard) = 2 : 5
Ken : (Archie + Howard) = 1 : 3
Howard has 16 pens more than Ken. In the end, Howard gives away all he has to Ken and Archie so that both Ken and Archie end up with the same number of pens, how many pens has Archie received from Howard?
Ken |
Howard |
Archie |
Total |
3x4 |
2x4 |
5x4 |
1x5 |
3x5 |
4x5 |
5 u |
7 u |
8 u |
20 u |
The total number of pens is repeated. Make the total number of pens the same. LCM of 5 and 4 is 20.
Number of pens that Howard has more than Ken
= 7 u - 5 u
= 2 u
2 u = 16
1 u = 16 ÷ 2 = 8
|
Ken |
Howard |
Archie |
Before |
5 u |
7 u |
8 u |
Change |
+ 5 u |
- 7 u |
+ 2 u |
After |
10 u |
0 u |
10 u |
Number of pens that Archie has received from Howard
= 10 u - 8 u
= 2 u
= 2 x 8
= 16
Answer(s): 16