Henry and John had some marbles in the ratio of 12 : 7. John and Carl had some marbles in the ratio of 10 : 3. Henry sold 1020 marbles to Carl and ended up with half the number of marbles John had. How many marbles did Carl have in the end?
| Henry |
John |
Carl |
| 12x10 |
7x10 |
|
| |
10x7 |
3x7 |
| 120 u |
70 u |
21 u |
The number of marbles that John had at first is repeated. Make the number of marbles that John had at first the same. LCM of 7 and 10 is 70.
| |
Henry |
John |
Carl |
| Before |
120 u |
70 u |
21 u |
| Change |
- 1020 |
|
+ 1020 |
| After |
35 u |
70 u |
21 u + 1020 |
Number of marbles that Henry had in the end
= 70 u ÷ 2
= 35 u
Number of marbles that Henry sold to Carl
= 120 u - 35 u
= 85 u
85 u = 1020
1 u = 1020 ÷ 85 = 12
Number of marbles that Carl had in the end
= 21 u + 1020
= 21 x 12 + 1020
= 252 + 1020
= 1272
Answer(s): 1272
