Jean and Yoko had 864 pens altogether. They decided to play a game. In the first round, Yoko lost 65 pens to Jean. In the second round, Jean lost 36 pens to Yoko. At the end of the two rounds, Yoko had five times as many pens as Jean.
- How many pens did Jean have in the end?
- How many pens did Yoko have at the beginning of the game?
|
Jean |
Yoko |
Total |
Before |
1 u + 36 - 65 |
5 u - 36 + 65 |
864 |
Round 1 |
+ 65 |
- 65 |
|
Round 2 |
- 36 |
+ 36 |
|
After |
1 u |
5 u |
864 |
(a)
Total number of pens
= 1 u + 5 u
= 6 u
6 u = 864
1 u = 864 ÷ 6 = 144
Number of pens that Jean had in the end
= 1 u
= 144
(b)
Working backwards.
Number of pens that Yoko had at the end of round 2
= 5 u
= 5 x 144
= 720
Number of pens that Yoko had at the end of round 1
= 720 - 36
= 684
Number of pens that Yoko had at the beginning of the game
= 684 + 65
= 749
Answer(s): (a) 144; (b) 749