Diana and Hilda had 810 stamps altogether. They decided to play a game. In the first round, Hilda lost 57 stamps to Diana. In the second round, Diana lost 36 stamps to Hilda. At the end of the two rounds, Hilda had five times as many stamps as Diana.
- How many stamps did Diana have in the end?
- How many stamps did Hilda have at the beginning of the game?
|
Diana |
Hilda |
Total |
Before |
1 u + 36 - 57 |
5 u - 36 + 57 |
810 |
Round 1 |
+ 57 |
- 57 |
|
Round 2 |
- 36 |
+ 36 |
|
After |
1 u |
5 u |
810 |
(a)
Total number of stamps
= 1 u + 5 u
= 6 u
6 u = 810
1 u = 810 ÷ 6 = 135
Number of stamps that Diana had in the end
= 1 u
= 135
(b)
Working backwards.
Number of stamps that Hilda had at the end of round 2
= 5 u
= 5 x 135
= 675
Number of stamps that Hilda had at the end of round 1
= 675 - 36
= 639
Number of stamps that Hilda had at the beginning of the game
= 639 + 57
= 696
Answer(s): (a) 135; (b) 696