Zane, Cody and George had a total of 46 marbles. The ratio of the number of marbles that Cody had to the number of marbles that George had was 2 : 9. After Zane and Cody each gave away half of their marbles, the 3 children had 32 marbles left. How many marbles did Cody and George have in the end?
| |
Zane |
Cody |
George |
Total |
| Before |
2 p |
2 u |
9 u |
46 |
| Change |
- 1 p |
- 1 u |
|
- 14 |
| After |
1 p |
1 u |
9 u |
32 |
Total number of marbles that Zane and Cody gave away
= 46 - 32
= 14
1 p + 1 u = 14 --- (1)
1 p + 1 u + 9 u = 32
1 p + 10 u = 32 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 32 - 14
10 u - 1 u = 18
9 u = 18
1 u = 18 ÷ 9 = 2
Total number of marbles that Cody and George had in the end
= 1 u + 9 u
= 10 u
= 10 x 2
= 20
Answer(s): 20
