Xuan and Min had 840 beads altogether. They decided to play a game. In the first round, Min lost 52 beads to Xuan. In the second round, Xuan lost 37 beads to Min. At the end of the two rounds, Min had six times as many beads as Xuan.
- How many beads did Xuan have in the end?
- How many beads did Min have at the beginning of the game?
|
Xuan |
Min |
Total |
Before |
1 u + 37 - 52 |
6 u - 37 + 52 |
840 |
Round 1 |
+ 52 |
- 52 |
|
Round 2 |
- 37 |
+ 37 |
|
After |
1 u |
6 u |
840 |
(a)
Total number of beads
= 1 u + 6 u
= 7 u
7 u = 840
1 u = 840 ÷ 7 = 120
Number of beads that Xuan had in the end
= 1 u
= 120
(b)
Working backwards.
Number of beads that Min had at the end of round 2
= 6 u
= 6 x 120
= 720
Number of beads that Min had at the end of round 1
= 720 - 37
= 683
Number of beads that Min had at the beginning of the game
= 683 + 52
= 735
Answer(s): (a) 120; (b) 735