Abi and Anna had 861 pens altogether. They decided to play a game. In the first round, Anna lost 53 pens to Abi. In the second round, Abi lost 36 pens to Anna. At the end of the two rounds, Anna had twice as many pens as Abi.
- How many pens did Abi have in the end?
- How many pens did Anna have at the beginning of the game?
| |
Abi |
Anna |
Total |
| Before |
1 u + 36 - 53 |
2 u - 36 + 53 |
861 |
| Round 1 |
+ 53 |
- 53 |
|
| Round 2 |
- 36 |
+ 36 |
|
| After |
1 u |
2 u |
861 |
(a)
Total number of pens
= 1 u + 2 u
= 3 u
3 u = 861
1 u = 861 ÷ 3 = 287
Number of pens that Abi had in the end
= 1 u
= 287
(b)
Working backwards.
Number of pens that Anna had at the end of round 2
= 2 u
= 2 x 287
= 574
Number of pens that Anna had at the end of round 1
= 574 - 36
= 538
Number of pens that Anna had at the beginning of the game
= 538 + 53
= 591
Answer(s): (a) 287; (b) 591
