Valen, Jack and Archie had the same number of beads. Archie gave 0.6 of his beads to Jack. Then Jack gave 0.25 of his beads to Valen. Finally, after Jack gave 36 beads to Archie, he had the same number of beads as Archie. How many beads did Archie have at first?
| |
Valen |
Jack |
Archie |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.6 u |
- 0.6 u |
| After 1 |
1 u |
1.6 u |
0.4 u |
| Change 2 |
+ 0.4 u |
- 0.4 u |
|
| After 2 |
1.4 u |
1.2 u |
0.4 u |
| Change 3 |
|
- 36 |
+ 36 |
| After 3 |
1.4 u |
1.2 u - 36 |
0.4 u + 36 |
Number of beads that Jack gave to Valen
= 0.25 x 1.6 u
= 0.4 u
The number of beads that Jack and Archie had in the end is the same.
1.2 u - 36 = 0.4 u + 36
1.2 u - 0.4 u = 36 + 36
0.8 u = 72
1 u = 72 ÷ 0.8 = 90
Number of beads that Archie had at first
= 1 u
= 90
Answer(s): 90
