SOLUTION: A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number. Show solut

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Question 1118053: A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number. Show solution
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
t, the tens digit
u, the ones digit
system%2810t%2Bu=1%2B6%28t%2Bu%29%2Ct%2B10u=%2810t%2Bu%29-9%29

Simplify and solve.

system%284t-5u=1%2Ct-u=1%29

Use second equation for t in terms of u.
t=u%2B1

Substitute into first equation.
4%28u%2B1%29-5u=1
.
.
system%28u=3%2Cand%2Ct=4%29

The number: highlight%2843%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


When a 2-digit number is reversed and the difference between the original number and the new number is calculated, it is always 9 times the difference between the two digits:

%2810t%2Bu%29-%2810u%2Bt%29+=+10t%2Bu-10u-t+=+9t-9u+=+9%28t-u%29

So in your problem, since the difference between the two numbers is 9, you know that the tens digit is 1 more than the units digit:
t+=+u%2B1%29

If an algebraic solution is required, then you can use that equation along with the one that says the number is 1 more than 6 times the sum of its digits to finish the problem:

t+=+u%2B1; 10t%2Bu+=+6%28t%2Bu%29%2B1

Or if you aren't required to show an algebraic solution, then simply look at all the 2-digit numbers that have the tens digit 1 more than the units digit and find the one for which the number is 1 more than 6 times the sum of its digits.