Usha and Kimberly had 840 pens altogether. They decided to play a game. In the first round, Kimberly lost 54 pens to Usha. In the second round, Usha lost 34 pens to Kimberly. At the end of the two rounds, Kimberly had six times as many pens as Usha.
- How many pens did Usha have in the end?
- How many pens did Kimberly have at the beginning of the game?
|
Usha |
Kimberly |
Total |
Before |
1 u + 34 - 54 |
6 u - 34 + 54 |
840 |
Round 1 |
+ 54 |
- 54 |
|
Round 2 |
- 34 |
+ 34 |
|
After |
1 u |
6 u |
840 |
(a)
Total number of pens
= 1 u + 6 u
= 7 u
7 u = 840
1 u = 840 ÷ 7 = 120
Number of pens that Usha had in the end
= 1 u
= 120
(b)
Working backwards.
Number of pens that Kimberly had at the end of round 2
= 6 u
= 6 x 120
= 720
Number of pens that Kimberly had at the end of round 1
= 720 - 34
= 686
Number of pens that Kimberly had at the beginning of the game
= 686 + 54
= 740
Answer(s): (a) 120; (b) 740