Zane had 180 more marbles than Gabriel. Zane gave 25% of his marbles to Gabriel. Gabriel in return gave 80% of his marbles to Zane. In the end, Gabriel had 370 less marbles than Zane. How many marbles did Zane have at first?
| |
Zane |
Gabriel |
Comparing Zane
and Peter at first |
180 more |
|
| Before |
4 u + 180 |
4 u |
| Change 1 |
- 1 u - 45 |
+ 1 u + 45 |
| After 1 |
3 u + 135 |
5 u + 45 |
| Change 2 |
+ 4 u + 36 |
- 4 u - 36 |
| After 2 |
7 u + 171 |
1 u + 9 |
25% =
25100 =
1425% x 180
=
25100 x 180
= 45
80% x 45
=
80100 x 45
= 36
80% x 5 u
=
80100 x 5 u
= 4 u
Gabriel had 370 less marbles than Zane in the end. If another 370 marbles are given to Gabriel, both will have the same number of marbles.
7 u + 171 = 1 u + 9 + 370
7 u - 1 u = 9 + 370 - 171
6 u = 208
1 u = 208 ÷ 6 = 26
Number of Gabriel's marbles at first
= 4 u
= 4 x 26
= 104
Answer: 104
