Usha and Hazel had 828 cards altogether. They decided to play a game. In the first round, Hazel lost 51 cards to Usha. In the second round, Usha lost 36 cards to Hazel. At the end of the two rounds, Hazel had five times as many cards as Usha.
- How many cards did Usha have in the end?
- How many cards did Hazel have at the beginning of the game?
|
Usha |
Hazel |
Total |
Before |
1 u + 36 - 51 |
5 u - 36 + 51 |
828 |
Round 1 |
+ 51 |
- 51 |
|
Round 2 |
- 36 |
+ 36 |
|
After |
1 u |
5 u |
828 |
(a)
Total number of cards
= 1 u + 5 u
= 6 u
6 u = 828
1 u = 828 ÷ 6 = 138
Number of cards that Usha had in the end
= 1 u
= 138
(b)
Working backwards.
Number of cards that Hazel had at the end of round 2
= 5 u
= 5 x 138
= 690
Number of cards that Hazel had at the end of round 1
= 690 - 36
= 654
Number of cards that Hazel had at the beginning of the game
= 654 + 51
= 705
Answer(s): (a) 138; (b) 705