Jeremy and Brandon collected some coins. If Jeremy gave Brandon 54 coins, both would have an equal number of coins. If Brandon gave Jeremy 36 coins, Jeremy would have 5 times as many coins as Brandon. Find the number of coins each of them had.
- Jeremy?
- Brandon?
| Case 1 |
Case 2 |
| Jeremy |
Brandon |
Jeremy |
Brandon |
| 3 u + 54 |
3 u - 54 |
5 u - 36 |
1 u + 36 |
| - 54 |
+ 54 |
+ 36 |
- 36 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of coins the same. LCM of 2 and 6 is 6.
The number of coins that Brandon had at first is the same in both cases.
3 u - 54 = 1 u + 36
3 u - 1 u = 54 + 36
2 u = 90
1 u = 90 ÷ 2 = 45
Number of coins that Jeremy had
= 3 u + 54
= 3 x 45 + 54
= 189
(b)
Number of coins that Brandon had
= 3 u - 54
= 3 x 45 - 54
= 81
Answer(s): (a) 189; (b) 81
