Tammy and Jen had 825 erasers altogether. They decided to play a game. In the first round, Jen lost 64 erasers to Tammy. In the second round, Tammy lost 40 erasers to Jen. At the end of the two rounds, Jen had four times as many erasers as Tammy.
- How many erasers did Tammy have in the end?
- How many erasers did Jen have at the beginning of the game?
|
Tammy |
Jen |
Total |
Before |
1 u + 40 - 64 |
4 u - 40 + 64 |
825 |
Round 1 |
+ 64 |
- 64 |
|
Round 2 |
- 40 |
+ 40 |
|
After |
1 u |
4 u |
825 |
(a)
Total number of erasers
= 1 u + 4 u
= 5 u
5 u = 825
1 u = 825 ÷ 5 = 165
Number of erasers that Tammy had in the end
= 1 u
= 165
(b)
Working backwards.
Number of erasers that Jen had at the end of round 2
= 4 u
= 4 x 165
= 660
Number of erasers that Jen had at the end of round 1
= 660 - 40
= 620
Number of erasers that Jen had at the beginning of the game
= 620 + 64
= 684
Answer(s): (a) 165; (b) 684