Xavier, Elijah and Rael had the same number of marbles. Rael gave 0.5 of his marbles to Elijah. Then Elijah gave 0.25 of his marbles to Xavier. Finally, after Elijah gave 30 marbles to Rael, he had the same number of marbles as Rael. How many marbles did Rael have at first?
| |
Xavier |
Elijah |
Rael |
| 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 |
+ 0.375 u |
- 0.375 u |
|
| After 2 |
1.375 u |
1.125 u |
0.5 u |
| Change 3 |
|
- 30 |
+ 30 |
| After 3 |
1.375 u |
1.125 u - 30 |
0.5 u + 30 |
Number of marbles that Elijah gave to Xavier
= 0.25 x 1.5 u
= 0.375 u
The number of marbles that Elijah and Rael had in the end is the same.
1.125 u - 30 = 0.5 u + 30
1.125 u - 0.5 u = 30 + 30
0.625 u = 60
1 u = 60 ÷ 0.625 = 96
Number of marbles that Rael had at first
= 1 u
= 96
Answer(s): 96
