Question 982373: when the tens digit of three digit number abc deleted a two digit number ac is formed. How many numbers abc are thee such that abc = 9ac+4c?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! when the tens digit of three digit number abc deleted a two digit number ac is formed.
How many numbers abc are there such that abc = 9ac+4c?
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the equation representing the 3 digit and 2 digit number
100a + 10b + c = 9(10a+c) + 4c
There are 3 unknowns here, let's assume that c=5, then we can simplify.
100a + 10b + 5 = 9(10a+5) + 4(5)
100a + 10b + 5 = 90a + 45 + 20
100a - 90a + 10b = 65 - 5
10a + 10b = 60
simplify, divide by 10
a + b = 6
How many 3 digit numbers can we have from this, assuming c = 5?
ABC
155
245
335
425
515
605
At least 6 numbers will satisfy our initial requirement
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I confirmed this with a little basic program I wrote, these are the only numbers that will work
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