Ivan and David collected some stickers. If Ivan gave David 57 stickers, both would have an equal number of stickers. If David gave Ivan 43 stickers, Ivan would have 6 times as many stickers as David. Find the number of stickers each of them had.
- Ivan?
- David?
| Case 1 |
Case 2 |
| Ivan |
David |
Ivan |
David |
| 7 u + 57 |
7 u - 57 |
12 u - 43 |
2 u + 43 |
| - 57 |
+ 57 |
+ 43 |
- 43 |
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 stickers the same. LCM of 2 and 7 is 14.
The number of stickers that David had at first is the same in both cases.
7 u - 57 = 2 u + 43
7 u - 2 u = 57 + 43
5 u = 100
1 u = 100 ÷ 5 = 20
Number of stickers that Ivan had
= 7 u + 57
= 7 x 20 + 57
= 197
(b)
Number of stickers that David had
= 7 u - 57
= 7 x 20 - 57
= 83
Answer(s): (a) 197; (b) 83
