Luis and Gabriel collected some coins. If Luis gave Gabriel 66 coins, both would have an equal number of coins. If Gabriel gave Luis 34 coins, Luis would have 6 times as many coins as Gabriel. Find the number of coins each of them had.
- Luis?
- Gabriel?
| Case 1 |
Case 2 |
| Luis |
Gabriel |
Luis |
Gabriel |
| 7 u + 66 |
7 u - 66 |
12 u - 34 |
2 u + 34 |
| - 66 |
+ 66 |
+ 34 |
- 34 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 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 7 is 14.
The number of coins that Gabriel had at first is the same in both cases.
7 u - 66 = 2 u + 34
7 u - 2 u = 66 + 34
5 u = 100
1 u = 100 ÷ 5 = 20
Number of coins that Luis had
= 7 u + 66
= 7 x 20 + 66
= 206
(b)
Number of coins that Gabriel had
= 7 u - 66
= 7 x 20 - 66
= 74
Answer(s): (a) 206; (b) 74
