Min and Jane had 825 marbles altogether. They decided to play a game. In the first round, Jane lost 64 marbles to Min. In the second round, Min lost 33 marbles to Jane. At the end of the two rounds, Jane had twice as many marbles as Min.
- How many marbles did Min have in the end?
- How many marbles did Jane have at the beginning of the game?
| |
Min |
Jane |
Total |
| Before |
1 u + 33 - 64 |
2 u - 33 + 64 |
825 |
| Round 1 |
+ 64 |
- 64 |
|
| Round 2 |
- 33 |
+ 33 |
|
| After |
1 u |
2 u |
825 |
(a)
Total number of marbles
= 1 u + 2 u
= 3 u
3 u = 825
1 u = 825 ÷ 3 = 275
Number of marbles that Min had in the end
= 1 u
= 275
(b)
Working backwards.
Number of marbles that Jane had at the end of round 2
= 2 u
= 2 x 275
= 550
Number of marbles that Jane had at the end of round 1
= 550 - 33
= 517
Number of marbles that Jane had at the beginning of the game
= 517 + 64
= 581
Answer(s): (a) 275; (b) 581
