Shannon and Yoko had 852 cards altogether. They decided to play a game. In the first round, Yoko lost 60 cards to Shannon. In the second round, Shannon lost 30 cards to Yoko. At the end of the two rounds, Yoko had thrice as many cards as Shannon.
- How many cards did Shannon have in the end?
- How many cards did Yoko have at the beginning of the game?
|
Shannon |
Yoko |
Total |
Before |
1 u + 30 - 60 |
3 u - 30 + 60 |
852 |
Round 1 |
+ 60 |
- 60 |
|
Round 2 |
- 30 |
+ 30 |
|
After |
1 u |
3 u |
852 |
(a)
Total number of cards
= 1 u + 3 u
= 4 u
4 u = 852
1 u = 852 ÷ 4 = 213
Number of cards that Shannon had in the end
= 1 u
= 213
(b)
Working backwards.
Number of cards that Yoko had at the end of round 2
= 3 u
= 3 x 213
= 639
Number of cards that Yoko had at the end of round 1
= 639 - 30
= 609
Number of cards that Yoko had at the beginning of the game
= 609 + 60
= 669
Answer(s): (a) 213; (b) 669