Nick and Tommy had some cards in the ratio of 11 : 10. Tommy and Caden had some cards in the ratio of 3 : 1. Nick sold 54 cards to Caden and ended up with half the number of cards Tommy had. How many cards did Caden have in the end?
| Nick |
Tommy |
Caden |
| 11x3 |
10x3 |
|
| |
3x10 |
1x10 |
| 33 u |
30 u |
10 u |
The number of cards that Tommy had at first is repeated. Make the number of cards that Tommy had at first the same. LCM of 10 and 3 is 30.
| |
Nick |
Tommy |
Caden |
| Before |
33 u |
30 u |
10 u |
| Change |
- 54 |
|
+ 54 |
| After |
15 u |
30 u |
10 u + 54 |
Number of cards that Nick had in the end
= 30 u ÷ 2
= 15 u
Number of cards that Nick sold to Caden
= 33 u - 15 u
= 18 u
18 u = 54
1 u = 54 ÷ 18 = 3
Number of cards that Caden had in the end
= 10 u + 54
= 10 x 3 + 54
= 30 + 54
= 84
Answer(s): 84
