SOLUTION: The sum of the digits of a two-digit number is 13. The tens digit is seventeen less than the square of the units digit. Find the number.

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: The sum of the digits of a two-digit number is 13. The tens digit is seventeen less than the square of the units digit. Find the number.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1186991: The sum of the digits of a two-digit number is 13. The tens digit is seventeen
less than the square of the units digit. Find the number.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
The sum of the digits of a two-digit number is 13. The tens digit is seventeen
less than the square of the units digit. Find the number.
~~~~~~~~~~~~~ 

Let x be the units digot.

Then the tens digit is 13-x, according to the condition.


Write an equation as you read the problem

    13-x = x^2 - 17.


Simplify and solve

    x^2 + x - 30 = 0

    (x-5)*(x+6) = 0


The only root, which fits as a solution to the problem is  x = 5.


The number is  85.     ANSWER

Solved.

-------------

Check it on your own that all requirements of the problem are satisfied.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
u and t
ONES digit and tens digit

system%28u%2Bt=13%2Ct=u%5E2-17%29

Looking at the formula for t, the second equation and taking only from the digits,
4%3Ct%3C10, so very few choices can be examined to see how they fit.

Try 5 for u ?
t=5%5E2-18
t=8
-
u%2Bt=13
u%2B8=13
u=5
-

The two digit number: 85