Ken and Eric collected some erasers. If Ken gave Eric 70 erasers, both would have an equal number of erasers. If Eric gave Ken 45 erasers, Ken would have 6 times as many erasers as Eric. Find the number of erasers each of them had.
- Ken?
- Eric?
| Case 1 |
Case 2 |
| Ken |
Eric |
Ken |
Eric |
| 7 u + 70 |
7 u - 70 |
12 u - 45 |
2 u + 45 |
| - 70 |
+ 70 |
+ 45 |
- 45 |
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 Eric had at first is the same in both cases.
7 u - 70 = 2 u + 45
7 u - 2 u = 70 + 45
5 u = 115
1 u = 115 ÷ 5 = 23
Number of erasers that Ken had
= 7 u + 70
= 7 x 23 + 70
= 231
(b)
Number of erasers that Eric had
= 7 u - 70
= 7 x 23 - 70
= 91
Answer(s): (a) 231; (b) 91
