Riordan, Liam and Fred have some pens. The ratios of their pens are as follows:
Riordan : (Riordan + Liam + Fred) = 1 : 5
Liam : (Riordan + Fred) = 1 : 3
Fred has 66 pens more than Liam. In the end, Fred gives away all he has to Liam and Riordan so that both Liam and Riordan end up with the same number of pens, how many pens has Liam received from Fred?
Liam |
Fred |
Riordan |
Total |
4x4 |
1x4 |
5x4 |
1x5 |
3x5 |
4x5 |
5 u |
11 u |
4 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 Fred has more than Liam
= 11 u - 5 u
= 6 u
6 u = 66
1 u = 66 ÷ 6 = 11
|
Liam |
Fred |
Riordan |
Before |
5 u |
11 u |
4 u |
Change |
+ 5 u |
- 11 u |
+ 6 u |
After |
10 u |
0 u |
10 u |
Number of pens that Liam has received from Fred
= 10 u - 5 u
= 5 u
= 5 x 11
= 55
Answer(s): 55