Ken and Glen collected some pens. If Ken gave Glen 61 pens, both would have an equal number of pens. If Glen gave Ken 41 pens, Ken would have 4 times as many pens as Glen. Find the number of pens each of them had.
- Ken?
- Glen?
| Case 1 |
Case 2 |
| Ken |
Glen |
Ken |
Glen |
| 5 u + 61 |
5 u - 61 |
8 u - 41 |
2 u + 41 |
| - 61 |
+ 61 |
+ 41 |
- 41 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of pens the same. LCM of 2 and 5 is 10.
The number of pens that Glen had at first is the same in both cases.
5 u - 61 = 2 u + 41
5 u - 2 u = 61 + 41
3 u = 102
1 u = 102 ÷ 3 = 34
Number of pens that Ken had
= 5 u + 61
= 5 x 34 + 61
= 231
(b)
Number of pens that Glen had
= 5 u - 61
= 5 x 34 - 61
= 109
Answer(s): (a) 231; (b) 109
