Gabriel and Justin collected some coins. If Gabriel gave Justin 60 coins, both would have an equal number of coins. If Justin gave Gabriel 30 coins, Gabriel would have 5 times as many coins as Justin. Find the number of coins each of them had.
- Gabriel?
- Justin?
| Case 1 |
Case 2 |
| Gabriel |
Justin |
Gabriel |
Justin |
| 3 u + 60 |
3 u - 60 |
5 u - 30 |
1 u + 30 |
| - 60 |
+ 60 |
+ 30 |
- 30 |
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 Justin had at first is the same in both cases.
3 u - 60 = 1 u + 30
3 u - 1 u = 60 + 30
2 u = 90
1 u = 90 ÷ 2 = 45
Number of coins that Gabriel had
= 3 u + 60
= 3 x 45 + 60
= 195
(b)
Number of coins that Justin had
= 3 u - 60
= 3 x 45 - 60
= 75
Answer(s): (a) 195; (b) 75
