Fred, Andy and Valen had a total of 30 marbles. The ratio of the number of marbles that Andy had to the number of marbles that Valen had was 2 : 5. After Fred and Andy each gave away half of their marbles, the 3 children had 20 marbles left. How many marbles did Andy and Valen have in the end?
| |
Fred |
Andy |
Valen |
Total |
| Before |
2 p |
2 u |
5 u |
30 |
| Change |
- 1 p |
- 1 u |
|
- 10 |
| After |
1 p |
1 u |
5 u |
20 |
Total number of marbles that Fred and Andy gave away
= 30 - 20
= 10
1 p + 1 u = 10 --- (1)
1 p + 1 u + 5 u = 20
1 p + 6 u = 20 --- (2)
(2) - (1)
(1 p + 6 u) - (1 p + 1 u) = 20 - 10
6 u - 1 u = 10
5 u = 10
1 u = 10 ÷ 5 = 2
Total number of marbles that Andy and Valen had in the end
= 1 u + 5 u
= 6 u
= 6 x 2
= 12
Answer(s): 12
