Min and Dana had 889 beads altogether. They decided to play a game. In the first round, Dana lost 51 beads to Min. In the second round, Min lost 30 beads to Dana. At the end of the two rounds, Dana had six times as many beads as Min.
- How many beads did Min have in the end?
- How many beads did Dana have at the beginning of the game?
| |
Min |
Dana |
Total |
| Before |
1 u + 30 - 51 |
6 u - 30 + 51 |
889 |
| Round 1 |
+ 51 |
- 51 |
|
| Round 2 |
- 30 |
+ 30 |
|
| After |
1 u |
6 u |
889 |
(a)
Total number of beads
= 1 u + 6 u
= 7 u
7 u = 889
1 u = 889 ÷ 7 = 127
Number of beads that Min had in the end
= 1 u
= 127
(b)
Working backwards.
Number of beads that Dana had at the end of round 2
= 6 u
= 6 x 127
= 762
Number of beads that Dana had at the end of round 1
= 762 - 30
= 732
Number of beads that Dana had at the beginning of the game
= 732 + 51
= 783
Answer(s): (a) 127; (b) 783
