Cody and Ryan collected some marbles. If Cody gave Ryan 64 marbles, both would have an equal number of marbles. If Ryan gave Cody 44 marbles, Cody would have 4 times as many marbles as Ryan. Find the number of marbles each of them had.
- Cody?
- Ryan?
| Case 1 |
Case 2 |
| Cody |
Ryan |
Cody |
Ryan |
| 5 u + 64 |
5 u - 64 |
8 u - 44 |
2 u + 44 |
| - 64 |
+ 64 |
+ 44 |
- 44 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of marbles the same. LCM of 2 and 5 is 10.
The number of marbles that Ryan had at first is the same in both cases.
5 u - 64 = 2 u + 44
5 u - 2 u = 64 + 44
3 u = 108
1 u = 108 ÷ 3 = 36
Number of marbles that Cody had
= 5 u + 64
= 5 x 36 + 64
= 244
(b)
Number of marbles that Ryan had
= 5 u - 64
= 5 x 36 - 64
= 116
Answer(s): (a) 244; (b) 116
