Howard had 50 more marbles than Oliver. Howard gave 20% of his marbles to Oliver. Oliver in return gave 50% of his marbles to Howard. In the end, Oliver had 82 less marbles than Howard. How many marbles did Howard have at first?
| |
Howard |
Oliver |
Comparing Howard
and Peter at first |
50 more |
|
| Before |
5 u + 50 |
5 u |
| Change 1 |
- 1 u - 10 |
+ 1 u + 10 |
| After 1 |
4 u + 40 |
6 u + 10 |
| Change 2 |
+ 3 u + 5 |
- 3 u - 5 |
| After 2 |
7 u + 45 |
3 u + 5 |
20% =
20100 =
1520% x 50
=
20100 x 50
= 10
50% x 10
=
50100 x 10
= 5
50% x 6 u
=
50100 x 6 u
= 3 u
Oliver had 82 less marbles than Howard in the end. If another 82 marbles are given to Oliver, both will have the same number of marbles.
7 u + 45 = 3 u + 5 + 82
7 u - 3 u = 5 + 82 - 45
4 u = 42
1 u = 42 ÷ 4 = 21
Number of Oliver's marbles at first
= 5 u
= 5 x 21
= 105
Answer: 105
