Answer
2.1 inches of rain
Work Step by Step
We write the system of equations:
$$ 2.47=(a)(4^2)+(4)(b)+c \\ .58=(a)(7^2)+(7)(b)+c \\ 1.07=(a)(8^2)+(8)(b)+c$$
We solve for a:
$$(a)(4^2)+(4)(b)+c \\ a=\frac{2.47-4b-c}{16}$$
Thus, in the second and third equations:
$$0.58=\frac{2.47-4b-c}{16}\cdot 7^2+7b+c \\ 1.07=\frac{2.47-4b-c}{16}\cdot 8^2+8b+c$$
So:
$$0.58=-5.25b-2.0625c+7.56 $$
Substituting b:
$$ c = 12.8 $$
Thus, plugging this into the equation for b:
$$ b = -3.71$$
Finally:
$$ a= .28$$
In September, which is the 9th month:
$$ y = (.28)(9^2)-3.71(9)+ 12.83 \\ y = 2.1 \ inches $$
