John, Luis and Billy have some pens. The ratios of their pens are as follows:
John : (John + Luis + Billy) = 3 : 7
Luis : (John + Billy) = 1 : 3
Billy has 12 pens more than Luis. In the end, Billy gives away all he has to Luis and John so that both Luis and John end up with the same number of pens, how many pens has John received from Billy?
Luis |
Billy |
John |
Total |
4x4 |
3x4 |
7x4 |
1x7 |
3x7 |
4x7 |
7 u |
9 u |
12 u |
28 u |
The total number of pens is repeated. Make the total number of pens the same. LCM of 7 and 4 is 28.
Number of pens that Billy has more than Luis
= 9 u - 7 u
= 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
|
Luis |
Billy |
John |
Before |
7 u |
9 u |
12 u |
Change |
+ 7 u |
- 9 u |
+ 2 u |
After |
14 u |
0 u |
14 u |
Number of pens that John has received from Billy
= 14 u - 12 u
= 2 u
= 2 x 6
= 12
Answer(s): 12