Winnie and Emily had 875 pens altogether. They decided to play a game. In the first round, Emily lost 57 pens to Winnie. In the second round, Winnie lost 40 pens to Emily. At the end of the two rounds, Emily had six times as many pens as Winnie.
- How many pens did Winnie have in the end?
- How many pens did Emily have at the beginning of the game?
|
Winnie |
Emily |
Total |
Before |
1 u + 40 - 57 |
6 u - 40 + 57 |
875 |
Round 1 |
+ 57 |
- 57 |
|
Round 2 |
- 40 |
+ 40 |
|
After |
1 u |
6 u |
875 |
(a)
Total number of pens
= 1 u + 6 u
= 7 u
7 u = 875
1 u = 875 ÷ 7 = 125
Number of pens that Winnie had in the end
= 1 u
= 125
(b)
Working backwards.
Number of pens that Emily had at the end of round 2
= 6 u
= 6 x 125
= 750
Number of pens that Emily had at the end of round 1
= 750 - 40
= 710
Number of pens that Emily had at the beginning of the game
= 710 + 57
= 767
Answer(s): (a) 125; (b) 767