Glen and Tom had some cards in the ratio of 5 : 3. Tom and John had some cards in the ratio of 2 : 1. Glen sold 84 cards to John and ended up with half the number of cards Tom had. How many cards did John have in the end?
| Glen |
Tom |
John |
| 5x2 |
3x2 |
|
| |
2x3 |
1x3 |
| 10 u |
6 u |
3 u |
The number of cards that Tom had at first is repeated. Make the number of cards that Tom had at first the same. LCM of 3 and 2 is 6.
| |
Glen |
Tom |
John |
| Before |
10 u |
6 u |
3 u |
| Change |
- 84 |
|
+ 84 |
| After |
3 u |
6 u |
3 u + 84 |
Number of cards that Glen had in the end
= 6 u ÷ 2
= 3 u
Number of cards that Glen sold to John
= 10 u - 3 u
= 7 u
7 u = 84
1 u = 84 ÷ 7 = 12
Number of cards that John had in the end
= 3 u + 84
= 3 x 12 + 84
= 36 + 84
= 120
Answer(s): 120
