Vincent and Seth collected some pens. If Vincent gave Seth 61 pens, both would have an equal number of pens. If Seth gave Vincent 35 pens, Vincent would have 5 times as many pens as Seth. Find the number of pens each of them had.
- Vincent?
- Seth?
| Case 1 |
Case 2 |
| Vincent |
Seth |
Vincent |
Seth |
| 3 u + 61 |
3 u - 61 |
5 u - 35 |
1 u + 35 |
| - 61 |
+ 61 |
+ 35 |
- 35 |
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 Seth had at first is the same in both cases.
3 u - 61 = 1 u + 35
3 u - 1 u = 61 + 35
2 u = 96
1 u = 96 ÷ 2 = 48
Number of pens that Vincent had
= 3 u + 61
= 3 x 48 + 61
= 205
(b)
Number of pens that Seth had
= 3 u - 61
= 3 x 48 - 61
= 83
Answer(s): (a) 205; (b) 83
