Jack and Sam had some cards in the ratio of 5 : 2. Sam and Owen had some cards in the ratio of 5 : 1. Jack sold 120 cards to Owen and ended up with half the number of cards Sam had. How many cards did Owen have in the end?
| Jack |
Sam |
Owen |
| 5x5 |
2x5 |
|
| |
5x2 |
1x2 |
| 25 u |
10 u |
2 u |
The number of cards that Sam had at first is repeated. Make the number of cards that Sam had at first the same. LCM of 2 and 5 is 10.
| |
Jack |
Sam |
Owen |
| Before |
25 u |
10 u |
2 u |
| Change |
- 120 |
|
+ 120 |
| After |
5 u |
10 u |
2 u + 120 |
Number of cards that Jack had in the end
= 10 u ÷ 2
= 5 u
Number of cards that Jack sold to Owen
= 25 u - 5 u
= 20 u
20 u = 120
1 u = 120 ÷ 20 = 6
Number of cards that Owen had in the end
= 2 u + 120
= 2 x 6 + 120
= 12 + 120
= 132
Answer(s): 132
