Wesley and Ethan collected some cards. If Wesley gave Ethan 65 cards, both would have an equal number of cards. If Ethan gave Wesley 37 cards, Wesley would have 4 times as many cards as Ethan. Find the number of cards each of them had.
- Wesley?
- Ethan?
| Case 1 |
Case 2 |
| Wesley |
Ethan |
Wesley |
Ethan |
| 5 u + 65 |
5 u - 65 |
8 u - 37 |
2 u + 37 |
| - 65 |
+ 65 |
+ 37 |
- 37 |
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 cards the same. LCM of 2 and 5 is 10.
The number of cards that Ethan had at first is the same in both cases.
5 u - 65 = 2 u + 37
5 u - 2 u = 65 + 37
3 u = 102
1 u = 102 ÷ 3 = 34
Number of cards that Wesley had
= 5 u + 65
= 5 x 34 + 65
= 235
(b)
Number of cards that Ethan had
= 5 u - 65
= 5 x 34 - 65
= 105
Answer(s): (a) 235; (b) 105
