David and Albert had some marbles in the ratio of 11 : 6. Albert and Paul had some marbles in the ratio of 8 : 1. David sold 352 marbles to Paul and ended up with half the number of marbles Albert had. How many marbles did Paul have in the end?
| David |
Albert |
Paul |
| 11x4 |
6x4 |
|
| |
8x3 |
1x3 |
| 44 u |
24 u |
3 u |
The number of marbles that Albert had at first is repeated. Make the number of marbles that Albert had at first the same. LCM of 6 and 8 is 24.
| |
David |
Albert |
Paul |
| Before |
44 u |
24 u |
3 u |
| Change |
- 352 |
|
+ 352 |
| After |
12 u |
24 u |
3 u + 352 |
Number of marbles that David had in the end
= 24 u ÷ 2
= 12 u
Number of marbles that David sold to Paul
= 44 u - 12 u
= 32 u
32 u = 352
1 u = 352 ÷ 32 = 11
Number of marbles that Paul had in the end
= 3 u + 352
= 3 x 11 + 352
= 33 + 352
= 385
Answer(s): 385
