Glen and John collected some marbles. If Glen gave John 59 marbles, both would have an equal number of marbles. If John gave Glen 36 marbles, Glen would have 6 times as many marbles as John. Find the number of marbles each of them had.
- Glen?
- John?
| Case 1 |
Case 2 |
| Glen |
John |
Glen |
John |
| 7 u + 59 |
7 u - 59 |
12 u - 36 |
2 u + 36 |
| - 59 |
+ 59 |
+ 36 |
- 36 |
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 marbles the same. LCM of 2 and 7 is 14.
The number of marbles that John had at first is the same in both cases.
7 u - 59 = 2 u + 36
7 u - 2 u = 59 + 36
5 u = 95
1 u = 95 ÷ 5 = 19
Number of marbles that Glen had
= 7 u + 59
= 7 x 19 + 59
= 192
(b)
Number of marbles that John had
= 7 u - 59
= 7 x 19 - 59
= 74
Answer(s): (a) 192; (b) 74
