Albert, Liam and Owen shared a bag of marbles. Liam took 27 as many marbles as Owen. Albert took twice as many marbles as the total Liam and Owen took. After Albert had given 80 to Liam and 10 to Owen, Liam gave 10 to Owen. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Albert and Liam had at first.
| |
Liam |
Owen |
Albert |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 80 |
|
- 80 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of marbles that Liam and Owen had at first
= 2 u + 7 u
= 9 u
Number of marbles that Albert had at first
= 2 x 9 u
= 18 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 27 is 27.
Number of marbles that Owen received from Liam and Albert
= 9 u - 7 u
= 2 u
2 u = 10 + 10
2 u = 20
1 u = 20 ÷ 2 = 10
Difference between the number marbles that Albert and Liam had at first
= 18 u - 2 u
= 16 u
= 16 x 10
= 160
Answer(s): 160
