A man had to pack a sack of apples into packets but as each packet had to have exactly the same number of apples he was having difficulty. If he packed 10 apples per packet, one packet only had 9. If he packed 9 apples per packet, one packet only had 8. If he packed 8 apples per packet, one packet only had 7. If he packed 7 apples per packet, one packet only had 6. And so on down to 2 apples. How many apples did he start with?
2006-06-27 08:59:13 · 9 answers · asked by Anonymous in Education & Reference ➔ Trivia
2519.
For every packing situation, if you had one more apple, the total number of apples would be an even multiple. So you want a number that is one less than a multiple of 10 and is one less than a multiple of 9 and...
To find this number, take the LCM of 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1, which is 2520.
Then subtract one.
(I found the LCM by factoring each number: 10 is 5x2, 9 is 3x3, etc. Then multiply these factors: 2x5x3x3x2x2x7)
2006-06-27 09:10:36 · answer #1 · answered by I eat apples 2 · 1⤊ 0⤋
Let x be the total number of apples. Since you are one apple short of having a number of packets with 10 each, x+1 is a multiple of 10. By the same logic, x+1 is a multiple of
10, 9, 8, 7, 6, 5, 4, 3, and 2. (10 is a multiple of 5 and 2, and 8 is a multiple of 4 and 2, and 6 is a multiple of 3 and 2, so you don't really need to worry about them.)
What number is a multiple of 10, 9, 8, 7, and 6? Look at the prime factors...it'll be 5*2*3*3*2*2*7. The answer is 2,520. Since you are one apple short of that, you have 2,519 apples.
Check:
251 packets of 10 + 9 apples = 2,519.
279 packets of 9 + 8 apples = 2,519.
314 packets of 8 + 7 apples = 2,519.
359 packets of 7 + 6 apples = 2,519.
419 packets of 6 + 5 apples = 2,519.
503 packets of 5 + 4 apples = 2,519.
629 packets of 4 + 3 apples = 2,519.
839 packets of 3 + 2 apples = 2,519.
1,259 packets of 2 + 1 apple = 2,519.
2006-06-27 16:10:24 · answer #2 · answered by -j. 7 · 0⤊ 0⤋
19
2006-06-27 17:07:56 · answer #3 · answered by yo 2 · 0⤊ 0⤋
That is a lot of apples to pack. Did he ever get tired?
2006-06-28 11:50:36 · answer #4 · answered by OliveTheCat 2 · 0⤊ 0⤋
I think that the man started with 5039 apples.
5039 divided by 10 gives you a remainder of 9
5039 divided by 9 gives you a remainder of 8
5039 divided by 8 gives you a remainder of 7
5039 divided by 7 gives you a remainder of 6
5039 divided by 6 gives you a remainder of 5
5039 divided by 5 gives you a remainder of 4
5039 divided by 4 gives you a remainder of 3
5039 divided by 3 gives you a remainder of 2
5039 divided by 2 gives you a remainder of 1
2006-06-27 17:16:08 · answer #5 · answered by Charles G 1 · 0⤊ 0⤋
he should have just made apple juice
2006-06-27 16:38:28 · answer #6 · answered by Anonymous · 0⤊ 0⤋
one too few
2006-06-27 16:23:26 · answer #7 · answered by thegreatgaetano2 2 · 0⤊ 0⤋
i have no idea
2006-06-27 16:02:45 · answer #8 · answered by Laura Lovehagle 3 · 0⤊ 0⤋
just pick 1 more apple duh
2006-06-27 17:34:29 · answer #9 · answered by croc.rock 2 · 0⤊ 0⤋