Luis and Jack collected some marbles. If Luis gave Jack 66 marbles, both would have an equal number of marbles. If Jack gave Luis 30 marbles, Luis would have 5 times as many marbles as Jack. Find the number of marbles each of them had.
- Luis?
- Jack?
| Case 1 |
Case 2 |
| Luis |
Jack |
Luis |
Jack |
| 3 u + 66 |
3 u - 66 |
5 u - 30 |
1 u + 30 |
| - 66 |
+ 66 |
+ 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 marbles the same. LCM of 2 and 6 is 6.
The number of marbles that Jack had at first is the same in both cases.
3 u - 66 = 1 u + 30
3 u - 1 u = 66 + 30
2 u = 96
1 u = 96 ÷ 2 = 48
Number of marbles that Luis had
= 3 u + 66
= 3 x 48 + 66
= 210
(b)
Number of marbles that Jack had
= 3 u - 66
= 3 x 48 - 66
= 78
Answer(s): (a) 210; (b) 78
