Harry and Bobby collected some pens. If Harry gave Bobby 54 pens, both would have an equal number of pens. If Bobby gave Harry 36 pens, Harry would have 4 times as many pens as Bobby. Find the number of pens each of them had.
- Harry?
- Bobby?
| Case 1 |
Case 2 |
| Harry |
Bobby |
Harry |
Bobby |
| 5 u + 54 |
5 u - 54 |
8 u - 36 |
2 u + 36 |
| - 54 |
+ 54 |
+ 36 |
- 36 |
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 Bobby had at first is the same in both cases.
5 u - 54 = 2 u + 36
5 u - 2 u = 54 + 36
3 u = 90
1 u = 90 ÷ 3 = 30
Number of pens that Harry had
= 5 u + 54
= 5 x 30 + 54
= 204
(b)
Number of pens that Bobby had
= 5 u - 54
= 5 x 30 - 54
= 96
Answer(s): (a) 204; (b) 96
