Opal and Sabrina had 820 beads altogether. They decided to play a game. In the first round, Sabrina lost 56 beads to Opal. In the second round, Opal lost 38 beads to Sabrina. At the end of the two rounds, Sabrina had thrice as many beads as Opal.
- How many beads did Opal have in the end?
- How many beads did Sabrina have at the beginning of the game?
|
Opal |
Sabrina |
Total |
Before |
1 u + 38 - 56 |
3 u - 38 + 56 |
820 |
Round 1 |
+ 56 |
- 56 |
|
Round 2 |
- 38 |
+ 38 |
|
After |
1 u |
3 u |
820 |
(a)
Total number of beads
= 1 u + 3 u
= 4 u
4 u = 820
1 u = 820 ÷ 4 = 205
Number of beads that Opal had in the end
= 1 u
= 205
(b)
Working backwards.
Number of beads that Sabrina had at the end of round 2
= 3 u
= 3 x 205
= 615
Number of beads that Sabrina had at the end of round 1
= 615 - 38
= 577
Number of beads that Sabrina had at the beginning of the game
= 577 + 56
= 633
Answer(s): (a) 205; (b) 633