Suppose the number f(x) of incidents of family violence requiring police response appears to be related to x, the money spent on crisis intervention, by the equation f(x) = 410 − 0.002x.

Question

What expenditure would reduce the number of incidents to 355?

Answer 1

To do this problem, we would just need to set f(x) equal to 355 like so:

355 = 410 - 0.002x

Then, we would subtract 410 from both sides, giving us:

-55 = -0.002x

Multiplying by -1 to simplify the expression, we then have:

55 = 0.002x

The last step is to divide both sides by 0.002. This gives us our solution:

x = 27,500

Assuming the units for x are dollars, the money spent to reduce family violence to 355 would be $27,500.