Emma and Irene had 830 cards altogether. They decided to play a game. In the first round, Irene lost 55 cards to Emma. In the second round, Emma lost 32 cards to Irene. At the end of the two rounds, Irene had four times as many cards as Emma.
- How many cards did Emma have in the end?
- How many cards did Irene have at the beginning of the game?
|
Emma |
Irene |
Total |
Before |
1 u + 32 - 55 |
4 u - 32 + 55 |
830 |
Round 1 |
+ 55 |
- 55 |
|
Round 2 |
- 32 |
+ 32 |
|
After |
1 u |
4 u |
830 |
(a)
Total number of cards
= 1 u + 4 u
= 5 u
5 u = 830
1 u = 830 ÷ 5 = 166
Number of cards that Emma had in the end
= 1 u
= 166
(b)
Working backwards.
Number of cards that Irene had at the end of round 2
= 4 u
= 4 x 166
= 664
Number of cards that Irene had at the end of round 1
= 664 - 32
= 632
Number of cards that Irene had at the beginning of the game
= 632 + 55
= 687
Answer(s): (a) 166; (b) 687