George and Brandon had some marbles in the ratio of 3 : 1. Brandon and Elijah had some marbles in the ratio of 10 : 3. George sold 300 marbles to Elijah and ended up with half the number of marbles Brandon had. How many marbles did Elijah have in the end?
| George |
Brandon |
Elijah |
| 3x10 |
1x10 |
|
| |
10x1 |
3x1 |
| 30 u |
10 u |
3 u |
The number of marbles that Brandon had at first is repeated. Make the number of marbles that Brandon had at first the same. LCM of 1 and 10 is 10.
| |
George |
Brandon |
Elijah |
| Before |
30 u |
10 u |
3 u |
| Change |
- 300 |
|
+ 300 |
| After |
5 u |
10 u |
3 u + 300 |
Number of marbles that George had in the end
= 10 u ÷ 2
= 5 u
Number of marbles that George sold to Elijah
= 30 u - 5 u
= 25 u
25 u = 300
1 u = 300 ÷ 25 = 12
Number of marbles that Elijah had in the end
= 3 u + 300
= 3 x 12 + 300
= 36 + 300
= 336
Answer(s): 336
