Elijah had 60 more marbles than Fred. Elijah gave 25% of his marbles to Fred. Fred in return gave 80% of his marbles to Elijah. In the end, Elijah had 102 more marbles than Fred. How many marbles did Elijah have at first?
| |
Elijah |
Fred |
Comparing Elijah
and Peter at first |
60 more |
|
| Before |
4 u + 60 |
4 u |
| Change 1 |
- 1 u - 15 |
+ 1 u + 15 |
| After 1 |
3 u + 45 |
5 u + 15 |
| Change 2 |
+ 4 u + 12 |
- 4 u - 12 |
| After 2 |
7 u + 57 |
1 u + 3 |
25% =
25100 =
1425% x 60
=
25100 x 60
= 15
80% x 15
=
80100 x 15
= 12
80% x 5 u
=
80100 x 5 u
= 4 u
Elijah had 102 more marbles than Fred in the end. If another 102 marbles are given to Fred, both will have the same number of marbles.
7 u + 57 = 1 u + 3 + 102
7 u - 1 u = 3 + 102 - 57
2 u = 48
1 u = 48 ÷ 2 = 24
Number of Elijah's marbles at first
= 4 u + 60
= 4 x 24 + 60
= 96 + 60
= 156
Answer: 156
