Eva and Jane had 804 coins altogether. They decided to play a game. In the first round, Jane lost 60 coins to Eva. In the second round, Eva lost 35 coins to Jane. At the end of the two rounds, Jane had twice as many coins as Eva.
- How many coins did Eva have in the end?
- How many coins did Jane have at the beginning of the game?
| |
Eva |
Jane |
Total |
| Before |
1 u + 35 - 60 |
2 u - 35 + 60 |
804 |
| Round 1 |
+ 60 |
- 60 |
|
| Round 2 |
- 35 |
+ 35 |
|
| After |
1 u |
2 u |
804 |
(a)
Total number of coins
= 1 u + 2 u
= 3 u
3 u = 804
1 u = 804 ÷ 3 = 268
Number of coins that Eva had in the end
= 1 u
= 268
(b)
Working backwards.
Number of coins that Jane had at the end of round 2
= 2 u
= 2 x 268
= 536
Number of coins that Jane had at the end of round 1
= 536 - 35
= 501
Number of coins that Jane had at the beginning of the game
= 501 + 60
= 561
Answer(s): (a) 268; (b) 561
