Henry had 200 more buttons than Ian. Henry gave 20% of his buttons to Ian. Ian in return gave 50% of his buttons to Henry. In the end, Henry had 823 more buttons than Ian. How many buttons did Henry have at first?
| |
Henry |
Ian |
Comparing Henry
and Peter at first |
200 more |
|
| Before |
5 u + 200 |
5 u |
| Change 1 |
- 1 u - 40 |
+ 1 u + 40 |
| After 1 |
4 u + 160 |
6 u + 40 |
| Change 2 |
+ 3 u + 20 |
- 3 u - 20 |
| After 2 |
7 u + 180 |
3 u + 20 |
20% =
20100 =
1520% x 200
=
20100 x 200
= 40
50% x 40
=
50100 x 40
= 20
50% x 6 u
=
50100 x 6 u
= 3 u
Henry had 823 more buttons than Ian in the end. If another 823 buttons are given to Ian, both will have the same number of buttons.
7 u + 180 = 3 u + 20 + 823
7 u - 3 u = 20 + 823 - 180
17 u = 663
1 u = 663 ÷ 17 = 39
Number of Henry's buttons at first
= 5 u + 200
= 5 x 39 + 200
= 195 + 200
= 395
Answer: 395
