Math Is Fun Forum
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#1 2007-09-18 21:17:02
- notagenius
- Member
- Registered: 2007-09-18
- Posts: 2
problem
i gotta find an integer that starts with 7 and if that 7 is put at the end of the number it becomes 1/5 of the first number!!
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#2 2007-09-18 21:40:32
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: problem
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#3 2007-09-18 22:09:31
- notagenius
- Member
- Registered: 2007-09-18
- Posts: 2
Re: problem
Jane, could you please tell me if there's a formula for it, so that it can be done without a calculator? I only got to the fact that every integer ending with 7 when multiplied has to end with 85 or 35, and if i want the number to begin with 7, i gotta have it start with 14... my brain is kinda stuck
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#4 2007-09-18 23:01:08
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: problem
The first number is 5 times the second number. So the first number is a multiple of 5 and so must end in 0 or 5. However, the second number is odd (it ends with in 7) and so the first number cant end in 0. Hence it ends in 5 and so the second number must end in 57.
5 × 57 = 285
∴ the first number ends in 285.
5 × 2857 = 14285
∴ the first number ends in 14285.
5 × 142857 = 714285
Bingo!
Last edited by JaneFairfax (2007-09-20 09:26:35)
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#5 2007-09-19 08:21:05
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: problem
I found another one but no 7 in this one:
1020408.16 x 5 = 50102040.8
Treat your calculator like a toy and keep trying
numbers that are just a little bit different from
the last and see if you can figure out how things
are changing. Sometimes jump a lot if you
want something new.
igloo myrtilles fourmis
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