Tommy had 180 more cards than Zeph. Tommy gave 20% of his cards to Zeph. Zeph in return gave 50% of his cards to Tommy. In the end, Tommy had 504 more cards than Zeph. How many cards did Tommy have at first?
| |
Tommy |
Zeph |
Comparing Tommy
and Peter at first |
180 more |
|
| Before |
5 u + 180 |
5 u |
| Change 1 |
- 1 u - 36 |
+ 1 u + 36 |
| After 1 |
4 u + 144 |
6 u + 36 |
| Change 2 |
+ 3 u + 18 |
- 3 u - 18 |
| After 2 |
7 u + 162 |
3 u + 18 |
20% =
20100 =
1520% x 180
=
20100 x 180
= 36
50% x 36
=
50100 x 36
= 18
50% x 6 u
=
50100 x 6 u
= 3 u
Tommy had 504 more cards than Zeph in the end. If another 504 cards are given to Zeph, both will have the same number of cards.
7 u + 162 = 3 u + 18 + 504
7 u - 3 u = 18 + 504 - 162
15 u = 360
1 u = 360 ÷ 15 = 24
Number of Tommy's cards at first
= 5 u + 180
= 5 x 24 + 180
= 120 + 180
= 300
Answer: 300
