Julian had 200 more buttons than Ben. Julian gave 20% of his buttons to Ben. Ben in return gave 50% of his buttons to Julian. In the end, Ben had 738 less buttons than Julian. How many buttons did Julian have at first?
| |
Julian |
Ben |
Comparing Julian
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
Ben had 738 less buttons than Julian in the end. If another 738 buttons are given to Ben, both will have the same number of buttons.
7 u + 180 = 3 u + 20 + 738
7 u - 3 u = 20 + 738 - 180
4 u = 578
1 u = 578 ÷ 4 = 34
Number of Ben's buttons at first
= 5 u
= 5 x 34
= 170
Answer: 170
