Xavier and Oscar collected some pens. If Xavier gave Oscar 68 pens, both would have an equal number of pens. If Oscar gave Xavier 34 pens, Xavier would have 5 times as many pens as Oscar. Find the number of pens each of them had.
- Xavier?
- Oscar?
| Case 1 |
Case 2 |
| Xavier |
Oscar |
Xavier |
Oscar |
| 3 u + 68 |
3 u - 68 |
5 u - 34 |
1 u + 34 |
| - 68 |
+ 68 |
+ 34 |
- 34 |
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 Oscar had at first is the same in both cases.
3 u - 68 = 1 u + 34
3 u - 1 u = 68 + 34
2 u = 102
1 u = 102 ÷ 2 = 51
Number of pens that Xavier had
= 3 u + 68
= 3 x 51 + 68
= 221
(b)
Number of pens that Oscar had
= 3 u - 68
= 3 x 51 - 68
= 85
Answer(s): (a) 221; (b) 85
