Simon, Elijah and Luke have some pens. The ratios of their pens are as follows:
Simon : (Simon + Elijah + Luke) = 2 : 5
Elijah : (Simon + Luke) = 1 : 3
Luke has 12 pens more than Elijah. In the end, Luke gives away all he has to Elijah and Simon so that both Elijah and Simon end up with the same number of pens, how many pens has Elijah received from Luke?
Elijah |
Luke |
Simon |
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 Luke has more than Elijah
= 7 u - 5 u
= 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
|
Elijah |
Luke |
Simon |
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 Elijah has received from Luke
= 10 u - 5 u
= 5 u
= 5 x 6
= 30
Answer(s): 30