Joelle and Jen had 894 beads altogether. They decided to play a game. In the first round, Jen lost 56 beads to Joelle. In the second round, Joelle lost 36 beads to Jen. At the end of the two rounds, Jen had five times as many beads as Joelle.
- How many beads did Joelle have in the end?
- How many beads did Jen have at the beginning of the game?
|
Joelle |
Jen |
Total |
Before |
1 u + 36 - 56 |
5 u - 36 + 56 |
894 |
Round 1 |
+ 56 |
- 56 |
|
Round 2 |
- 36 |
+ 36 |
|
After |
1 u |
5 u |
894 |
(a)
Total number of beads
= 1 u + 5 u
= 6 u
6 u = 894
1 u = 894 ÷ 6 = 149
Number of beads that Joelle had in the end
= 1 u
= 149
(b)
Working backwards.
Number of beads that Jen had at the end of round 2
= 5 u
= 5 x 149
= 745
Number of beads that Jen had at the end of round 1
= 745 - 36
= 709
Number of beads that Jen had at the beginning of the game
= 709 + 56
= 765
Answer(s): (a) 149; (b) 765