Brandon, Ethan and Simon had the same number of marbles. Simon gave 0.6 of his marbles to Ethan. Then Ethan gave 0.45 of his marbles to Brandon. Finally, after Ethan gave 24 marbles to Simon, he had the same number of marbles as Simon. How many marbles did Simon have at first?
| |
Brandon |
Ethan |
Simon |
| 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 |
+ 0.72 u |
- 0.72 u |
|
| After 2 |
1.72 u |
0.88 u |
0.4 u |
| Change 3 |
|
- 24 |
+ 24 |
| After 3 |
1.72 u |
0.88 u - 24 |
0.4 u + 24 |
Number of marbles that Ethan gave to Brandon
= 0.45 x 1.6 u
= 0.72 u
The number of marbles that Ethan and Simon had in the end is the same.
0.88 u - 24 = 0.4 u + 24
0.88 u - 0.4 u = 24 + 24
0.48 u = 48
1 u = 48 ÷ 0.48 = 100
Number of marbles that Simon had at first
= 1 u
= 100
Answer(s): 100
