Albert had 110 more beads than Pierre. Albert gave 20% of his beads to Pierre. Pierre in return gave 50% of his beads to Albert. In the end, Albert had 280 more beads than Pierre. How many beads did Albert have at first?
| |
Albert |
Pierre |
Comparing Albert
and Peter at first |
110 more |
|
| Before |
5 u + 110 |
5 u |
| Change 1 |
- 1 u - 22 |
+ 1 u + 22 |
| After 1 |
4 u + 88 |
6 u + 22 |
| Change 2 |
+ 3 u + 11 |
- 3 u - 11 |
| After 2 |
7 u + 99 |
3 u + 11 |
20% =
20100 =
1520% x 110
=
20100 x 110
= 22
50% x 22
=
50100 x 22
= 11
50% x 6 u
=
50100 x 6 u
= 3 u
Albert had 280 more beads than Pierre in the end. If another 280 beads are given to Pierre, both will have the same number of beads.
7 u + 99 = 3 u + 11 + 280
7 u - 3 u = 11 + 280 - 99
8 u = 192
1 u = 192 ÷ 8 = 24
Number of Albert's beads at first
= 5 u + 110
= 5 x 24 + 110
= 120 + 110
= 230
Answer: 230
