Yoko and Zoe had 897 beads altogether. They decided to play a game. In the first round, Zoe lost 53 beads to Yoko. In the second round, Yoko lost 36 beads to Zoe. At the end of the two rounds, Zoe had twice as many beads as Yoko.
- How many beads did Yoko have in the end?
- How many beads did Zoe have at the beginning of the game?
| |
Yoko |
Zoe |
Total |
| Before |
1 u + 36 - 53 |
2 u - 36 + 53 |
897 |
| Round 1 |
+ 53 |
- 53 |
|
| Round 2 |
- 36 |
+ 36 |
|
| After |
1 u |
2 u |
897 |
(a)
Total number of beads
= 1 u + 2 u
= 3 u
3 u = 897
1 u = 897 ÷ 3 = 299
Number of beads that Yoko had in the end
= 1 u
= 299
(b)
Working backwards.
Number of beads that Zoe had at the end of round 2
= 2 u
= 2 x 299
= 598
Number of beads that Zoe had at the end of round 1
= 598 - 36
= 562
Number of beads that Zoe had at the beginning of the game
= 562 + 53
= 615
Answer(s): (a) 299; (b) 615
