Question 300590: There is a boy named Regan who collects baseball cards. He has between 2500 and 3000 cards Use the facts and divide to find how many he has. Facts: When the total number of cards in his collection is divided by two, the remainder is one. When the total is divided by 3, remainder = 2. When total is divided by 4, remainder = 3. When the total is divided by 5, remainder = 4. This pattern follows up to when the total is divided by 10, the remainder is 9.
Answer by Edwin McCravy(20054)   (Show Source):
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It has to end with 9 since when divided by 10 it leaves a remainder of 9.
Try 2509
1254
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2)2509
2508
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1 so when divided by 2 it leaves remainder 1
836
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3)2509
2508
----
1 so when divided by 3 it leaves remainder 1
No good. It has to leave a remainder of 2.
So we try the next integer ending with 9, or 2519
1259
-----
2)2519
2518
----
1 so when divided by 2 it leaves remainder 1
839
-----
3)2519
2517
----
2 so when divided by 3 it leaves remainder 2
629
-----
4)2519
2516
----
3 so when divided by 4 it leaves remainder 3
503
-----
5)2519
2515
----
4 so when divided by 5 it leaves remainder 4
419
-----
6)2519
2514
----
5 so when divided by 6 it leaves remainder 5
359
-----
7)2519
2513
----
6 so when divided by 7 it leaves remainder 6
314
-----
8)2519
2512
----
7 so when divided by 8 it leaves remainder 7
279
-----
9)2519
2511
----
8 so when divided by 9 it leaves remainder 8
251
-----
10)2519
2510
----
9 so when divided by 10 it leaves remainder 9
So the second number I tried that ended with 9 worked.
Edwin
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