Ryan and Ian had some cards in the ratio of 11 : 8. Ian and Tim had some cards in the ratio of 10 : 7. Ryan sold 420 cards to Tim and ended up with half the number of cards Ian had. How many cards did Tim have in the end?
| Ryan |
Ian |
Tim |
| 11x5 |
8x5 |
|
| |
10x4 |
7x4 |
| 55 u |
40 u |
28 u |
The number of cards that Ian had at first is repeated. Make the number of cards that Ian had at first the same. LCM of 8 and 10 is 40.
| |
Ryan |
Ian |
Tim |
| Before |
55 u |
40 u |
28 u |
| Change |
- 420 |
|
+ 420 |
| After |
20 u |
40 u |
28 u + 420 |
Number of cards that Ryan had in the end
= 40 u ÷ 2
= 20 u
Number of cards that Ryan sold to Tim
= 55 u - 20 u
= 35 u
35 u = 420
1 u = 420 ÷ 35 = 12
Number of cards that Tim had in the end
= 28 u + 420
= 28 x 12 + 420
= 336 + 420
= 756
Answer(s): 756
