Kylie and Opal had 852 beads altogether. They decided to play a game. In the first round, Opal lost 52 beads to Kylie. In the second round, Kylie lost 36 beads to Opal. At the end of the two rounds, Opal had five times as many beads as Kylie.
- How many beads did Kylie have in the end?
- How many beads did Opal have at the beginning of the game?
|
Kylie |
Opal |
Total |
Before |
1 u + 36 - 52 |
5 u - 36 + 52 |
852 |
Round 1 |
+ 52 |
- 52 |
|
Round 2 |
- 36 |
+ 36 |
|
After |
1 u |
5 u |
852 |
(a)
Total number of beads
= 1 u + 5 u
= 6 u
6 u = 852
1 u = 852 ÷ 6 = 142
Number of beads that Kylie had in the end
= 1 u
= 142
(b)
Working backwards.
Number of beads that Opal had at the end of round 2
= 5 u
= 5 x 142
= 710
Number of beads that Opal had at the end of round 1
= 710 - 36
= 674
Number of beads that Opal had at the beginning of the game
= 674 + 52
= 726
Answer(s): (a) 142; (b) 726