Bobby and Archie had some cards in the ratio of 8 : 5. Archie and Rael had some cards in the ratio of 4 : 3. Bobby sold 220 cards to Rael and ended up with half the number of cards Archie had. How many cards did Rael have in the end?
| Bobby |
Archie |
Rael |
| 8x4 |
5x4 |
|
| |
4x5 |
3x5 |
| 32 u |
20 u |
15 u |
The number of cards that Archie had at first is repeated. Make the number of cards that Archie had at first the same. LCM of 5 and 4 is 20.
| |
Bobby |
Archie |
Rael |
| Before |
32 u |
20 u |
15 u |
| Change |
- 220 |
|
+ 220 |
| After |
10 u |
20 u |
15 u + 220 |
Number of cards that Bobby had in the end
= 20 u ÷ 2
= 10 u
Number of cards that Bobby sold to Rael
= 32 u - 10 u
= 22 u
22 u = 220
1 u = 220 ÷ 22 = 10
Number of cards that Rael had in the end
= 15 u + 220
= 15 x 10 + 220
= 150 + 220
= 370
Answer(s): 370
