Owen, David and Liam have some erasers. The ratios of their erasers are as follows:
Owen : (Owen + David + Liam) = 2 : 5
David : (Owen + Liam) = 1 : 5
Liam has 80 erasers more than David. In the end, Liam gives away all he has to David and Owen so that both David and Owen end up with the same number of erasers, how many erasers has David received from Liam?
David |
Liam |
Owen |
Total |
3x6 |
2x6 |
5x6 |
1x5 |
5x5 |
6x5 |
5 u |
13 u |
12 u |
30 u |
The total number of erasers is repeated. Make the total number of erasers the same. LCM of 5 and 6 is 30.
Number of erasers that Liam has more than David
= 13 u - 5 u
= 8 u
8 u = 80
1 u = 80 ÷ 8 = 10
|
David |
Liam |
Owen |
Before |
5 u |
13 u |
12 u |
Change |
+ 10 u |
- 13 u |
+ 3 u |
After |
15 u |
0 u |
15 u |
Number of erasers that David has received from Liam
= 15 u - 5 u
= 10 u
= 10 x 10
= 100
Answer(s): 100