Question 56203: three of the house numbers on a street are consecutive odd integers. their sum contains three consecutive digits such that the middle digit is equal to the sum of the other two. find the three house numbers on the street
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! three of the house numbers on a street are consecutive odd integers. their sum contains three consecutive digits such that the middle digit is equal to the sum of the other two. find the three house numbers on the street
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This one is a bit complicated. Let me know if you don't understand the
development.
Let the three consec. odd digits be: 2x+1, 2x+3, 2x+5
Their sum is 6x+9
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The three digit number is a*10^2+b^10+c and b=(a+c)
But a,b,and c are consecutive numbers so, b=a+1, c=a+2
So the number is a*10^2+(2a+2)10+a+2 or 131a+22
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EQUATION:
6x+9=121a+22
6x=121a+13
This means that 121a+13 is a multiple of 6.
So, lookina at values of 121a+13 for different values of a you get:
If a=1, 121a+13=133----not a multiple of 6
If a=2, 121a+13 =255----not a multiple of 6
If a=3, 121a+13=376---not a multiple of 6
...
If a=6, 121a+13 = 618---this is a multiploe of 6
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So a = 6
Therefore the consecutive 3-digit number is 678
The sum of these digits is 6+7+8=21
So 6x+9=21
x=2
1st consecutive odd number is 2x+1=5
2nd is 7
3rd is 9
The house numbers are 5, 7, and 9
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Three of the house numbers on a street are consecutive odd integers.
x, (x+2), (x+4)
Their sum: x + x + 2 + x + 4 = 3x + 6
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Their sum contains three consecutive digits such that the middle digit is equal to the sum of the other two.
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At first glance one thinks that 3 consecutive digits, where the middle is the sum of the outer two does not exist, however, the word "contain" would indicate that they are consecutive, but not necessarily in consecutive order.
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Their are only two three digit numbers that would meet this requirement:
132 and 231: 132 is an even number so it has to be 231:
:
3x + 6 = 231
3x = 225
x = 75
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Our numbers are 75, 77, 79
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