Daniel had 80 more cards than Zeph. Daniel gave 20% of his cards to Zeph. Zeph in return gave 50% of his cards to Daniel. In the end, Daniel had 164 more cards than Zeph. How many cards did Daniel have at first?
| |
Daniel |
Zeph |
Comparing Daniel
and Peter at first |
80 more |
|
| Before |
5 u + 80 |
5 u |
| Change 1 |
- 1 u - 16 |
+ 1 u + 16 |
| After 1 |
4 u + 64 |
6 u + 16 |
| Change 2 |
+ 3 u + 8 |
- 3 u - 8 |
| After 2 |
7 u + 72 |
3 u + 8 |
20% =
20100 =
1520% x 80
=
20100 x 80
= 16
50% x 16
=
50100 x 16
= 8
50% x 6 u
=
50100 x 6 u
= 3 u
Daniel had 164 more cards than Zeph in the end. If another 164 cards are given to Zeph, both will have the same number of cards.
7 u + 72 = 3 u + 8 + 164
7 u - 3 u = 8 + 164 - 72
5 u = 100
1 u = 100 ÷ 5 = 20
Number of Daniel's cards at first
= 5 u + 80
= 5 x 20 + 80
= 100 + 80
= 180
Answer: 180
