Michael had 180 more beads than Daniel. Michael gave 20% of his beads to Daniel. Daniel in return gave 50% of his beads to Michael. In the end, Daniel had 564 less beads than Michael. How many beads did Michael have at first?
| |
Michael |
Daniel |
Comparing Michael
and Peter at first |
180 more |
|
| Before |
5 u + 180 |
5 u |
| Change 1 |
- 1 u - 36 |
+ 1 u + 36 |
| After 1 |
4 u + 144 |
6 u + 36 |
| Change 2 |
+ 3 u + 18 |
- 3 u - 18 |
| After 2 |
7 u + 162 |
3 u + 18 |
20% =
20100 =
1520% x 180
=
20100 x 180
= 36
50% x 36
=
50100 x 36
= 18
50% x 6 u
=
50100 x 6 u
= 3 u
Daniel had 564 less beads than Michael in the end. If another 564 beads are given to Daniel, both will have the same number of beads.
7 u + 162 = 3 u + 18 + 564
7 u - 3 u = 18 + 564 - 162
4 u = 420
1 u = 420 ÷ 4 = 28
Number of Daniel's beads at first
= 5 u
= 5 x 28
= 140
Answer: 140
