Xavier had 140 more buttons than Vincent. Xavier gave 25% of his buttons to Vincent. Vincent in return gave 80% of his buttons to Xavier. In the end, Xavier had 300 more buttons than Vincent. How many buttons did Xavier have at first?
| |
Xavier |
Vincent |
Comparing Xavier
and Peter at first |
140 more |
|
| Before |
4 u + 140 |
4 u |
| Change 1 |
- 1 u - 35 |
+ 1 u + 35 |
| After 1 |
3 u + 105 |
5 u + 35 |
| Change 2 |
+ 4 u + 28 |
- 4 u - 28 |
| After 2 |
7 u + 133 |
1 u + 7 |
25% =
25100 =
1425% x 140
=
25100 x 140
= 35
80% x 35
=
80100 x 35
= 28
80% x 5 u
=
80100 x 5 u
= 4 u
Xavier had 300 more buttons than Vincent in the end. If another 300 buttons are given to Vincent, both will have the same number of buttons.
7 u + 133 = 1 u + 7 + 300
7 u - 1 u = 7 + 300 - 133
6 u = 174
1 u = 174 ÷ 6 = 29
Number of Xavier's buttons at first
= 4 u + 140
= 4 x 29 + 140
= 116 + 140
= 256
Answer: 256
