Zane and Owen collected some pens. If Zane gave Owen 62 pens, both would have an equal number of pens. If Owen gave Zane 38 pens, Zane would have 6 times as many pens as Owen. Find the number of pens each of them had.
- Zane?
- Owen?
| Case 1 |
Case 2 |
| Zane |
Owen |
Zane |
Owen |
| 7 u + 62 |
7 u - 62 |
12 u - 38 |
2 u + 38 |
| - 62 |
+ 62 |
+ 38 |
- 38 |
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 pens the same. LCM of 2 and 7 is 14.
The number of pens that Owen had at first is the same in both cases.
7 u - 62 = 2 u + 38
7 u - 2 u = 62 + 38
5 u = 100
1 u = 100 ÷ 5 = 20
Number of pens that Zane had
= 7 u + 62
= 7 x 20 + 62
= 202
(b)
Number of pens that Owen had
= 7 u - 62
= 7 x 20 - 62
= 78
Answer(s): (a) 202; (b) 78
