Luis and Sam collected some pens. If Luis gave Sam 62 pens, both would have an equal number of pens. If Sam gave Luis 38 pens, Luis would have 5 times as many pens as Sam. Find the number of pens each of them had.
- Luis?
- Sam?
| Case 1 |
Case 2 |
| Luis |
Sam |
Luis |
Sam |
| 3 u + 62 |
3 u - 62 |
5 u - 38 |
1 u + 38 |
| - 62 |
+ 62 |
+ 38 |
- 38 |
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 Sam had at first is the same in both cases.
3 u - 62 = 1 u + 38
3 u - 1 u = 62 + 38
2 u = 100
1 u = 100 ÷ 2 = 50
Number of pens that Luis had
= 3 u + 62
= 3 x 50 + 62
= 212
(b)
Number of pens that Sam had
= 3 u - 62
= 3 x 50 - 62
= 88
Answer(s): (a) 212; (b) 88
