Luis and Luke collected some coins. If Luis gave Luke 70 coins, both would have an equal number of coins. If Luke gave Luis 30 coins, Luis would have 5 times as many coins as Luke. Find the number of coins each of them had.
- Luis?
- Luke?
| Case 1 |
Case 2 |
| Luis |
Luke |
Luis |
Luke |
| 3 u + 70 |
3 u - 70 |
5 u - 30 |
1 u + 30 |
| - 70 |
+ 70 |
+ 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 Luke had at first is the same in both cases.
3 u - 70 = 1 u + 30
3 u - 1 u = 70 + 30
2 u = 100
1 u = 100 ÷ 2 = 50
Number of coins that Luis had
= 3 u + 70
= 3 x 50 + 70
= 220
(b)
Number of coins that Luke had
= 3 u - 70
= 3 x 50 - 70
= 80
Answer(s): (a) 220; (b) 80
