SOLUTION: The sum of the digits of a three -digit number is 17. The ones degit is two more than the hundreds digit. The tens digit is one more than the hundreds digit. What is the number?

Algebra.Com
Question 88954: The sum of the digits of a three -digit number is 17. The ones degit is two more than the hundreds digit. The tens digit is one more than the hundreds digit. What is the number?
Found 2 solutions by Edwin McCravy, ptaylor:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Note: I changed your 17 in the first sentence to 18, because 
with 17, the digits come out with fractions, and digits cannot 
be fractions.

The sum of the digits of a three-digit number is 18. The ones 
digit is two more than the hundreds digit. The tens digit is 
one more than the hundreds digit. What is the number?

Let the leftmost digit be L  (that's called the "hundreds digit")
Let the middle digit be M    (that's called the "tens digit") 
Let the rightmost digit be R (that's called the "ones" digit)

>>...The sum of the digits of a three -digit number is 18...<<

That says:

L + M + R = 18 

>>...The ones digit is two more than the hundreds digit...<<

That says:

R = L + 2

>>...The tens digit is one more than the hundreds digit.,,<<

That says:

M = L + 1

So you have this syetem of equations:

L + M + R = 18
R = L + 2
M = L + 1

You might write the last two this way:

 L + M + R = 18
-L     + R =  2
-L + M     =  1

If you can't solve that system then post again.

Answer: L = 5, M = 6, R = 7 so the number is 567.

Edwin
Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
RE-CHECK YOUR PROBLEM. SOMETHING'S WRONG (AND IT COULD BE ME BUT I DOUBT IT)
Let x=the hundreds digit
Then x+1=the tens digit
And x+2=the ones digit
Now we are told that:
x+x+1+x+2=17 collect like terms
3x+3=17 subtract 3 from both sides
3x+3-3=17-3 collect like terms
3x=14 divide both sides by 3
x=4.666667 ??????????????????????????

Something's wrong. x should be a whole number.
If the sum was 18 instead of 17, then the problem has a solution (567)
x=5
x+1=6
x+2=7
5+6+7=18
18-18
Hope this helps----ptaylor



RELATED QUESTIONS

The sum of the digits of a three-digit number is 15. The ones digit is one less than the... (answered by lwsshak3)
The sum of the digits in a three-digit counting number is 17. The tens digit is 1 more... (answered by addingup)
The sum of the digits of a three-digit number is 13. The hundreds' digit is two more than (answered by vheroli)
my tens digit is two more than my ones digit and four less than my hundreds digit the sum (answered by josgarithmetic)
The sum of the digits of a three digit number is 14. The hundreds digit is 2 more than... (answered by schmidtmomto6)
in a 3-digit number, the hundreds digit is one half of the tens digit. The ones digit is... (answered by MathLover1,Edwin McCravy)
In a 3-digit number, the hundreds digit is one half of the tens digit. The ones digit is... (answered by josgarithmetic)
The sum of the digits of a certain three digit number is 12. If the hundreds digit is... (answered by stanbon)
In a 4-digit number the tens and hundreds digits are 3. The ones digit is twice the tens... (answered by Edwin McCravy)