Paul had 80 more pens than Gabriel. Paul gave 20% of his pens to Gabriel. Gabriel in return gave 50% of his pens to Paul. In the end, Paul had 229 more pens than Gabriel. How many pens did Paul have at first?
| |
Paul |
Gabriel |
Comparing Paul
and Peter at first |
80 more |
|
| Before |
5 u + 80 |
5 u |
| Change 1 |
- 1 u - 16 |
+ 1 u + 16 |
| After 1 |
4 u + 64 |
6 u + 16 |
| Change 2 |
+ 3 u + 8 |
- 3 u - 8 |
| After 2 |
7 u + 72 |
3 u + 8 |
20% =
20100 =
1520% x 80
=
20100 x 80
= 16
50% x 16
=
50100 x 16
= 8
50% x 6 u
=
50100 x 6 u
= 3 u
Paul had 229 more pens than Gabriel in the end. If another 229 pens are given to Gabriel, both will have the same number of pens.
7 u + 72 = 3 u + 8 + 229
7 u - 3 u = 8 + 229 - 72
5 u = 165
1 u = 165 ÷ 5 = 33
Number of Paul's pens at first
= 5 u + 80
= 5 x 33 + 80
= 165 + 80
= 245
Answer: 245
