Rael had 50 more erasers than Fred. Rael gave 20% of his erasers to Fred. Fred in return gave 50% of his erasers to Rael. In the end, Rael had 120 more erasers than Fred. How many erasers did Rael have at first?
| |
Rael |
Fred |
Comparing Rael
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
Rael had 120 more erasers than Fred in the end. If another 120 erasers are given to Fred, both will have the same number of erasers.
7 u + 45 = 3 u + 5 + 120
7 u - 3 u = 5 + 120 - 45
2 u = 80
1 u = 80 ÷ 2 = 40
Number of Rael's erasers at first
= 5 u + 50
= 5 x 40 + 50
= 200 + 50
= 250
Answer: 250
