Jeremy and Oliver had some cards in the ratio of 11 : 3. Oliver and Tommy had some cards in the ratio of 2 : 1. Jeremy sold 57 cards to Tommy and ended up with half the number of cards Oliver had. How many cards did Tommy have in the end?
| Jeremy |
Oliver |
Tommy |
| 11x2 |
3x2 |
|
| |
2x3 |
1x3 |
| 22 u |
6 u |
3 u |
The number of cards that Oliver had at first is repeated. Make the number of cards that Oliver had at first the same. LCM of 3 and 2 is 6.
| |
Jeremy |
Oliver |
Tommy |
| Before |
22 u |
6 u |
3 u |
| Change |
- 57 |
|
+ 57 |
| After |
3 u |
6 u |
3 u + 57 |
Number of cards that Jeremy had in the end
= 6 u ÷ 2
= 3 u
Number of cards that Jeremy sold to Tommy
= 22 u - 3 u
= 19 u
19 u = 57
1 u = 57 ÷ 19 = 3
Number of cards that Tommy had in the end
= 3 u + 57
= 3 x 3 + 57
= 9 + 57
= 66
Answer(s): 66
