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

6

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! :)