Lynn and Jen had 882 marbles altogether. They decided to play a game. In the first round, Jen lost 63 marbles to Lynn. In the second round, Lynn lost 31 marbles to Jen. At the end of the two rounds, Jen had five times as many marbles as Lynn.
- How many marbles did Lynn have in the end?
- How many marbles did Jen have at the beginning of the game?
|
Lynn |
Jen |
Total |
Before |
1 u + 31 - 63 |
5 u - 31 + 63 |
882 |
Round 1 |
+ 63 |
- 63 |
|
Round 2 |
- 31 |
+ 31 |
|
After |
1 u |
5 u |
882 |
(a)
Total number of marbles
= 1 u + 5 u
= 6 u
6 u = 882
1 u = 882 ÷ 6 = 147
Number of marbles that Lynn had in the end
= 1 u
= 147
(b)
Working backwards.
Number of marbles that Jen had at the end of round 2
= 5 u
= 5 x 147
= 735
Number of marbles that Jen had at the end of round 1
= 735 - 31
= 704
Number of marbles that Jen had at the beginning of the game
= 704 + 63
= 767
Answer(s): (a) 147; (b) 767