Liam, Simon and Archie had the same number of balls. Archie gave 0.5 of his balls to Simon. Then Simon gave 0.15 of his balls to Liam. Finally, after Simon gave 31 balls to Archie, he had the same number of balls as Archie. How many balls did Archie have at first?
| |
Liam |
Simon |
Archie |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.5 u |
- 0.5 u |
| After 1 |
1 u |
1.5 u |
0.5 u |
| Change 2 |
+ 0.225 u |
- 0.225 u |
|
| After 2 |
1.225 u |
1.275 u |
0.5 u |
| Change 3 |
|
- 31 |
+ 31 |
| After 3 |
1.225 u |
1.275 u - 31 |
0.5 u + 31 |
Number of balls that Simon gave to Liam
= 0.15 x 1.5 u
= 0.225 u
The number of balls that Simon and Archie had in the end is the same.
1.275 u - 31 = 0.5 u + 31
1.275 u - 0.5 u = 31 + 31
0.775 u = 62
1 u = 62 ÷ 0.775 = 80
Number of balls that Archie had at first
= 1 u
= 80
Answer(s): 80
