Fred and Reggie had some cards in the ratio of 5 : 1. Reggie and Tom had some cards in the ratio of 8 : 3. Fred sold 360 cards to Tom and ended up with half the number of cards Reggie had. How many cards did Tom have in the end?
| Fred |
Reggie |
Tom |
| 5x8 |
1x8 |
|
| |
8x1 |
3x1 |
| 40 u |
8 u |
3 u |
The number of cards that Reggie had at first is repeated. Make the number of cards that Reggie had at first the same. LCM of 1 and 8 is 8.
| |
Fred |
Reggie |
Tom |
| Before |
40 u |
8 u |
3 u |
| Change |
- 360 |
|
+ 360 |
| After |
4 u |
8 u |
3 u + 360 |
Number of cards that Fred had in the end
= 8 u ÷ 2
= 4 u
Number of cards that Fred sold to Tom
= 40 u - 4 u
= 36 u
36 u = 360
1 u = 360 ÷ 36 = 10
Number of cards that Tom had in the end
= 3 u + 360
= 3 x 10 + 360
= 30 + 360
= 390
Answer(s): 390
