Gabriel had 120 more cards than Lee. Gabriel gave 20% of his cards to Lee. Lee in return gave 50% of his cards to Gabriel. In the end, Gabriel had 429 more cards than Lee. How many cards did Gabriel have at first?
| |
Gabriel |
Lee |
Comparing Gabriel
and Peter at first |
120 more |
|
| Before |
5 u + 120 |
5 u |
| Change 1 |
- 1 u - 24 |
+ 1 u + 24 |
| After 1 |
4 u + 96 |
6 u + 24 |
| Change 2 |
+ 3 u + 12 |
- 3 u - 12 |
| After 2 |
7 u + 108 |
3 u + 12 |
20% =
20100 =
1520% x 120
=
20100 x 120
= 24
50% x 24
=
50100 x 24
= 12
50% x 6 u
=
50100 x 6 u
= 3 u
Gabriel had 429 more cards than Lee in the end. If another 429 cards are given to Lee, both will have the same number of cards.
7 u + 108 = 3 u + 12 + 429
7 u - 3 u = 12 + 429 - 108
9 u = 333
1 u = 333 ÷ 9 = 37
Number of Gabriel's cards at first
= 5 u + 120
= 5 x 37 + 120
= 185 + 120
= 305
Answer: 305
