Andy, Ethan and Mark had the same number of marbles. Mark gave 0.8 of his marbles to Ethan. Then Ethan gave 0.25 of his marbles to Andy. Finally, after Ethan gave 23 marbles to Mark, he had the same number of marbles as Mark. How many marbles did Mark have at first?
| |
Andy |
Ethan |
Mark |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.8 u |
- 0.8 u |
| After 1 |
1 u |
1.8 u |
0.2 u |
| Change 2 |
+ 0.45 u |
- 0.45 u |
|
| After 2 |
1.45 u |
1.35 u |
0.2 u |
| Change 3 |
|
- 23 |
+ 23 |
| After 3 |
1.45 u |
1.35 u - 23 |
0.2 u + 23 |
Number of marbles that Ethan gave to Andy
= 0.25 x 1.8 u
= 0.45 u
The number of marbles that Ethan and Mark had in the end is the same.
1.35 u - 23 = 0.2 u + 23
1.35 u - 0.2 u = 23 + 23
1.15 u = 46
1 u = 46 ÷ 1.15 = 40
Number of marbles that Mark had at first
= 1 u
= 40
Answer(s): 40
