Question 53086: My daughter got this word problem for school and it sounds pretty simple to me
but I have tried everything and I am horrible at math so I need a little help
before I throw my calculator out the window! Here is it
Linae went shopping for Kou-jong tiles at the local toy shop the other day. The kou-jong tiles were on sale for only 28 cents each.
However, she got it in her head that, for good luck, the total amount of money she must spend must be a number where all of the digits are the same.
With that in mind, what is the minimum number of tiles she must buy?
Found 3 solutions by consc198, ankor@dixie-net.com, ikleyn:
Answer by consc198(59)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! It's the amt she spends that has to be all the same digits, isn't it?
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All we have to do is find out what multiple of 28 has all the same digits.
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Acually between 100 and 1 million there is not that many. We know the number has to be even, no zeros obviously. Get a calculator and start with 222/28, then 444/28, etc. I got to 444444 and found that 28 goes evenly into it, 15873 times so this many tiles cost $4,444.44.
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Answer by ikleyn(53804)  (Show Source):
You can put this solution on YOUR website! .
My daughter got this word problem for school and it sounds pretty simple to me
but I have tried everything and I am horrible at math so I need a little help
before I throw my calculator out the window! Here is it
Linae went shopping for Kou-jong tiles at the local toy shop the other day.
The kou-jong tiles were on sale for only 28 cents each.
However, she got it in her head that, for good luck, the total amount of money
she must spend must be a number where all of the digits are the same.
With that in mind, what is the minimum number of tiles she must buy?
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The solution by @consc198 in his post is, OBVIOUSLY, wrong and irrelevant.
For a correct solution see what follows.
We want to have a positive integer number (the spent amount) where all the digits are the same,
and this number should be multiple of 28. The additional condition is that this number must be minimal possible.
Since this number is a multiple of 28, it should be a multiple of 4 and a multiple of 7.
It means that we should find a minimum possible number written by ones, '1', which is a multiple of 7.
Make "trial and error".
111 divided by 7 gives the remainder 6.
1111 divided by 7 gives the remainder 5.
11111 divided by 7 gives the remainder 2.
111111 divided by 7 gives the remainder 0: in other words, 111111 is a multiple of 7.
It implies that 444444 is a multiple of 28.
Thus the minimum number of tiles Linae should buy to satisfy the conditions is 444444/28 = 15873.
ANSWER. The minimum number of tiles Linae should buy to satisfy the conditions is 15873.
Solved.
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