Final answer:
To find the number, we can set up two equations based on the given information and solve them simultaneously. By substituting the value of one variable into the other equation, we can determine the values of both variables. The number is 29.
Step-by-step explanation:
To find the number, let's represent the tens digit as 'x' and the units digit as 'y'.
According to the given information, the tens digit is 7 less than the units digit, so we have the equation x = y - 7.
The sum of the squares of the two digits is 85, so we have the equation x^2 + y^2 = 85.
Substituting the value of x from the first equation into the second equation, we can solve for y: (y-7)^2 + y^2 = 85.
Expanding and simplifying the equation gives y^2 - 14y + 49 + y^2 = 85.
Combining like terms and rearranging, we get 2y^2 - 14y - 36 = 0.
Using the quadratic formula, we can solve for y: y = (-b +/- sqrt(b^2 - 4ac)) / (2a).
Plugging in the values a = 2, b = -14, and c = -36, we get y = 9 or y = -2.
Since we are dealing with digits, y cannot be negative, so y = 9. Substituting this value back into the equation x = y - 7, we get x = 9 - 7 = 2.
Therefore, the number is 29.