Luke and George had some cards in the ratio of 7 : 2. George and Zane had some cards in the ratio of 9 : 8. Luke sold 378 cards to Zane and ended up with half the number of cards George had. How many cards did Zane have in the end?
| Luke |
George |
Zane |
| 7x9 |
2x9 |
|
| |
9x2 |
8x2 |
| 63 u |
18 u |
16 u |
The number of cards that George had at first is repeated. Make the number of cards that George had at first the same. LCM of 2 and 9 is 18.
| |
Luke |
George |
Zane |
| Before |
63 u |
18 u |
16 u |
| Change |
- 378 |
|
+ 378 |
| After |
9 u |
18 u |
16 u + 378 |
Number of cards that Luke had in the end
= 18 u ÷ 2
= 9 u
Number of cards that Luke sold to Zane
= 63 u - 9 u
= 54 u
54 u = 378
1 u = 378 ÷ 54 = 7
Number of cards that Zane had in the end
= 16 u + 378
= 16 x 7 + 378
= 112 + 378
= 490
Answer(s): 490
