Oscar and Luis collected some erasers. If Oscar gave Luis 55 erasers, both would have an equal number of erasers. If Luis gave Oscar 37 erasers, Oscar would have 5 times as many erasers as Luis. Find the number of erasers each of them had.
- Oscar?
- Luis?
| Case 1 |
Case 2 |
| Oscar |
Luis |
Oscar |
Luis |
| 3 u + 55 |
3 u - 55 |
5 u - 37 |
1 u + 37 |
| - 55 |
+ 55 |
+ 37 |
- 37 |
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 erasers the same. LCM of 2 and 6 is 6.
The number of erasers that Luis had at first is the same in both cases.
3 u - 55 = 1 u + 37
3 u - 1 u = 55 + 37
2 u = 92
1 u = 92 ÷ 2 = 46
Number of erasers that Oscar had
= 3 u + 55
= 3 x 46 + 55
= 193
(b)
Number of erasers that Luis had
= 3 u - 55
= 3 x 46 - 55
= 83
Answer(s): (a) 193; (b) 83
