Daniel and Mark collected some pens. If Daniel gave Mark 61 pens, both would have an equal number of pens. If Mark gave Daniel 45 pens, Daniel would have 5 times as many pens as Mark. Find the number of pens each of them had.
- Daniel?
- Mark?
| Case 1 |
Case 2 |
| Daniel |
Mark |
Daniel |
Mark |
| 3 u + 61 |
3 u - 61 |
5 u - 45 |
1 u + 45 |
| - 61 |
+ 61 |
+ 45 |
- 45 |
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 pens the same. LCM of 2 and 6 is 6.
The number of pens that Mark had at first is the same in both cases.
3 u - 61 = 1 u + 45
3 u - 1 u = 61 + 45
2 u = 106
1 u = 106 ÷ 2 = 53
Number of pens that Daniel had
= 3 u + 61
= 3 x 53 + 61
= 220
(b)
Number of pens that Mark had
= 3 u - 61
= 3 x 53 - 61
= 98
Answer(s): (a) 220; (b) 98
