Charlie and Will had some cards in the ratio of 3 : 2. Will and David had some cards in the ratio of 5 : 1. Charlie sold 110 cards to David and ended up with half the number of cards Will had. How many cards did David have in the end?
| Charlie |
Will |
David |
| 3x5 |
2x5 |
|
| |
5x2 |
1x2 |
| 15 u |
10 u |
2 u |
The number of cards that Will had at first is repeated. Make the number of cards that Will had at first the same. LCM of 2 and 5 is 10.
| |
Charlie |
Will |
David |
| Before |
15 u |
10 u |
2 u |
| Change |
- 110 |
|
+ 110 |
| After |
5 u |
10 u |
2 u + 110 |
Number of cards that Charlie had in the end
= 10 u ÷ 2
= 5 u
Number of cards that Charlie sold to David
= 15 u - 5 u
= 10 u
10 u = 110
1 u = 110 ÷ 10 = 11
Number of cards that David had in the end
= 2 u + 110
= 2 x 11 + 110
= 22 + 110
= 132
Answer(s): 132
