Sean, Archie and George had a total of 72 marbles. The ratio of the number of marbles that Archie had to the number of marbles that George had was 2 : 3. After Sean and Archie each gave away half of their marbles, the 3 children had 54 marbles left. How many marbles did Archie and George have at first?
| |
Sean |
Archie |
George |
Total |
| Before |
2 p |
2 u |
3 u |
72 |
| Change |
- 1 p |
- 1 u |
|
- 18 |
| After |
1 p |
1 u |
3 u |
54 |
Total number of marbles that Sean and Archie gave away
= 72 - 54
= 18
1 p + 1 u = 18 --- (1)
1 p + 1 u + 3 u = 54
1 p + 4 u = 54 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 54 - 18
4 u - 1 u = 36
3 u = 36
1 u = 36 ÷ 3 = 12
Total number of marbles that Archie and George had at first
= 2 u + 3 u
= 5 u
= 5 x 12
= 60
Answer(s): 60
