Fred and Bobby collected some erasers. If Fred gave Bobby 65 erasers, both would have an equal number of erasers. If Bobby gave Fred 30 erasers, Fred would have 6 times as many erasers as Bobby. Find the number of erasers each of them had.
- Fred?
- Bobby?
| Case 1 |
Case 2 |
| Fred |
Bobby |
Fred |
Bobby |
| 7 u + 65 |
7 u - 65 |
12 u - 30 |
2 u + 30 |
| - 65 |
+ 65 |
+ 30 |
- 30 |
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 erasers the same. LCM of 2 and 7 is 14.
The number of erasers that Bobby had at first is the same in both cases.
7 u - 65 = 2 u + 30
7 u - 2 u = 65 + 30
5 u = 95
1 u = 95 ÷ 5 = 19
Number of erasers that Fred had
= 7 u + 65
= 7 x 19 + 65
= 198
(b)
Number of erasers that Bobby had
= 7 u - 65
= 7 x 19 - 65
= 68
Answer(s): (a) 198; (b) 68
