Perry, Cody and Elijah had the same number of marbles. Elijah gave 0.5 of his marbles to Cody. Then Cody gave 0.25 of his marbles to Perry. Finally, after Cody gave 20 marbles to Elijah, he had the same number of marbles as Elijah. How many marbles did Elijah have at first?
| |
Perry |
Cody |
Elijah |
| 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 |
|
- 20 |
+ 20 |
| After 3 |
1.375 u |
1.125 u - 20 |
0.5 u + 20 |
Number of marbles that Cody gave to Perry
= 0.25 x 1.5 u
= 0.375 u
The number of marbles that Cody and Elijah had in the end is the same.
1.125 u - 20 = 0.5 u + 20
1.125 u - 0.5 u = 20 + 20
0.625 u = 40
1 u = 40 ÷ 0.625 = 64
Number of marbles that Elijah had at first
= 1 u
= 64
Answer(s): 64
