Question

Eighty-five more than the square of a number is the same as the square of the quantity that is 17 less than the number. What is the number?

Answer 1

We can turn this word problem into the following equation:
x^2 + 85 = (x - 17)^2
  x^2 + 85 = x^2 - 34x + 289
           -85                       -85
_______________________
      x^2 = x^2 - 34x + 204                    
     +34x         +34x
_______________________
 x^2 + 34x = x^2 + 204
-x^2             -x^2
____________________
       34x = 204
Divide 34 on both sides
      x = 6.
The number is 6.

Answer 2

Answer:

6

Step-by-step explanation:

If the number is $x$, we set up the equation: $x^2+85=(x-17)^2$ and solve for $x$.

$\begin{align*}x^2+85&=(x-17)^2\quad\Rightarrow\end{align*}$$x^2+85=(x-17)^2$

$x^2+85=x^2-34x+289$

$34x=204$

$x=6$

Therefore, the number is $\boxed{6}$.

Hope this helped! :)