Xavier, Andy and Simon had a total of 19 marbles. The ratio of the number of marbles that Andy had to the number of marbles that Simon had was 2 : 3. After Xavier and Andy each gave away half of their marbles, the 3 children had 14 marbles left. How many marbles did Andy and Simon have at first?
| |
Xavier |
Andy |
Simon |
Total |
| Before |
2 p |
2 u |
3 u |
19 |
| Change |
- 1 p |
- 1 u |
|
- 5 |
| After |
1 p |
1 u |
3 u |
14 |
Total number of marbles that Xavier and Andy gave away
= 19 - 14
= 5
1 p + 1 u = 5 --- (1)
1 p + 1 u + 3 u = 14
1 p + 4 u = 14 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 14 - 5
4 u - 1 u = 9
3 u = 9
1 u = 9 ÷ 3 = 3
Total number of marbles that Andy and Simon had at first
= 2 u + 3 u
= 5 u
= 5 x 3
= 15
Answer(s): 15
