Zane had 70 more cards than Ben. Zane gave 20% of his cards to Ben. Ben in return gave 50% of his cards to Zane. In the end, Zane had 144 more cards than Ben. How many cards did Zane have at first?
| |
Zane |
Ben |
Comparing Zane
and Peter at first |
70 more |
|
| Before |
5 u + 70 |
5 u |
| Change 1 |
- 1 u - 14 |
+ 1 u + 14 |
| After 1 |
4 u + 56 |
6 u + 14 |
| Change 2 |
+ 3 u + 7 |
- 3 u - 7 |
| After 2 |
7 u + 63 |
3 u + 7 |
20% =
20100 =
1520% x 70
=
20100 x 70
= 14
50% x 14
=
50100 x 14
= 7
50% x 6 u
=
50100 x 6 u
= 3 u
Zane had 144 more cards than Ben in the end. If another 144 cards are given to Ben, both will have the same number of cards.
7 u + 63 = 3 u + 7 + 144
7 u - 3 u = 7 + 144 - 63
4 u = 88
1 u = 88 ÷ 4 = 22
Number of Zane's cards at first
= 5 u + 70
= 5 x 22 + 70
= 110 + 70
= 180
Answer: 180
