Fred and Albert collected some coins. If Fred gave Albert 63 coins, both would have an equal number of coins. If Albert gave Fred 33 coins, Fred would have 4 times as many coins as Albert. Find the number of coins each of them had.
- Fred?
- Albert?
| Case 1 |
Case 2 |
| Fred |
Albert |
Fred |
Albert |
| 5 u + 63 |
5 u - 63 |
8 u - 33 |
2 u + 33 |
| - 63 |
+ 63 |
+ 33 |
- 33 |
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 coins the same. LCM of 2 and 5 is 10.
The number of coins that Albert had at first is the same in both cases.
5 u - 63 = 2 u + 33
5 u - 2 u = 63 + 33
3 u = 96
1 u = 96 ÷ 3 = 32
Number of coins that Fred had
= 5 u + 63
= 5 x 32 + 63
= 223
(b)
Number of coins that Albert had
= 5 u - 63
= 5 x 32 - 63
= 97
Answer(s): (a) 223; (b) 97
