Peter had 100 more cards than Wesley. Peter gave 20% of his cards to Wesley. Wesley in return gave 50% of his cards to Peter. In the end, Peter had 269 more cards than Wesley. How many cards did Peter have at first?
| |
Peter |
Wesley |
Comparing Peter
and Peter at first |
100 more |
|
| Before |
5 u + 100 |
5 u |
| Change 1 |
- 1 u - 20 |
+ 1 u + 20 |
| After 1 |
4 u + 80 |
6 u + 20 |
| Change 2 |
+ 3 u + 10 |
- 3 u - 10 |
| After 2 |
7 u + 90 |
3 u + 10 |
20% =
20100 =
1520% x 100
=
20100 x 100
= 20
50% x 20
=
50100 x 20
= 10
50% x 6 u
=
50100 x 6 u
= 3 u
Peter had 269 more cards than Wesley in the end. If another 269 cards are given to Wesley, both will have the same number of cards.
7 u + 90 = 3 u + 10 + 269
7 u - 3 u = 10 + 269 - 90
7 u = 189
1 u = 189 ÷ 7 = 27
Number of Peter's cards at first
= 5 u + 100
= 5 x 27 + 100
= 135 + 100
= 235
Answer: 235
