Abi and Gabby had 832 erasers altogether. They decided to play a game. In the first round, Gabby lost 60 erasers to Abi. In the second round, Abi lost 32 erasers to Gabby. At the end of the two rounds, Gabby had thrice as many erasers as Abi.
- How many erasers did Abi have in the end?
- How many erasers did Gabby have at the beginning of the game?
| |
Abi |
Gabby |
Total |
| Before |
1 u + 32 - 60 |
3 u - 32 + 60 |
832 |
| Round 1 |
+ 60 |
- 60 |
|
| Round 2 |
- 32 |
+ 32 |
|
| After |
1 u |
3 u |
832 |
(a)
Total number of erasers
= 1 u + 3 u
= 4 u
4 u = 832
1 u = 832 ÷ 4 = 208
Number of erasers that Abi had in the end
= 1 u
= 208
(b)
Working backwards.
Number of erasers that Gabby had at the end of round 2
= 3 u
= 3 x 208
= 624
Number of erasers that Gabby had at the end of round 1
= 624 - 32
= 592
Number of erasers that Gabby had at the beginning of the game
= 592 + 60
= 652
Answer(s): (a) 208; (b) 652
